The most practical reason is Germany did not possess the naval resources for an invasion of Great Britain at any period of time during the war.

The German Navy had no suitable landing craft for a cross channel invasion so the plan was to use converted river barges for the crossing. This would have been disastrous not only because of the unpredictable seas in the channel, but also because of the lack of sufficient numbers of German war ships to secure their crossing. The Royal Navy would have annihilated the invasion force long before they got close to the English coast.

Hitler wasnt actually willing to sacrifice that many men and materials in 1941. The Russian experience in the Russo-Finnish War (the Winter War) seemed to prove that the Russians were incapable of waging an effective defense against a Nazi attack, using the same armies which had just beaten France (considered, in 1940, one of the most powerful armies in Europe). The Wehrmacht and Hitler felt that they could repeat their success in 1941 by encircling the Russian Army along the inter-Polish border, destroying it, then quickly seizing Moscow. The idea was, the Red Army would be overwhelmed and destroyed, leaving the rest of Russia defenseless. But, contrary to expectations the Red Army fought tenaciously, and while it gave ground, it cost the Germans heavily. Further, the Germans were not as good destroying the Red Army as had been predicted. The titanic scale of the invasion meant that there was a lot of space between German units. While the Wehrmacht was very good at stopping Regiments, Brigades, and Divisions (large units) from escaping encirclement, many Russians were able to pass through German lines and return to service for the winter campaign. Further, the Russians were able to mobilize a massive segment of its population for war service, especially post-1942. Those losses that the Germans inflicted (which were substantial) could eventually be replaced by fresh soldiers, and new, domestic, weapons.

Hitler didnt really count on any of that in 1941. He expected the campaign to end before the fall of 1941, and the German army, sans a garrison force, would be able to return to Germany that year. He was merely committing himself to employing the Army for the summer, not launching on a titanic 4 year campaign which would destroy Germany. By the winter of 1941, it was obvious that the invasion had not succeeded, but by then it was already too late. War was declared, and the Red Army would not simply go away.

As for a Cross Channel invasion, I suppose I hold a contrarian view on Operation SeaLion. We could get into that, if youd like, and if we can keep it civil. But by 1941, there wasnt any real chance of a Cross Channel invasion without some serious changes in the German War effort. The Kriegsmarine was smashed, and the Luftwaffe had been badly handled during the Battle of Britain. Further, the British Army was fully recovered from their Dunkirk evacuation, and were remarkably prepared for any sort of invasion. So, from that perspective too, Barbarossa made some sense. Getting at England from France would have been a pain in the Ass. But Russia, (seemingly)weak Russia, shared a common border with Germany.

There were also philosophical or world view reasons.

Hitler utterly despised the Soviet Union, and catastrophically underestimated the Soviet ability to put up a fight. He has been quoted as saying: You only need to kick in the (Soviet) door, and the whole building will come crashing down".

He also had a sort of half baked "plan" of forcing England to sue for peace by conquering the S.U. He reasoned that the S.U. was England's last "ally" and hope on the continent, and by knocking them out, England would lose hope and sue for peace.

So, in his own head, Hitler thought that the easiest way to defeat England was to knock The S.U out.

Personally, I have my doubts whether he actually believed this, or if it was just a way to avoid invading England, a task he admittedly feared.

The huge losses on the Eastern front came as a very nasty surprise. The plan was to defeat the S.U by christmas. The invasion started in June, and most everyone expected it to be a walkover...

Operation Barbarossa was planned to carry out a swift land grab, with combat ending by Fall at the latest and pursuit following after. Hitler and the military commanders and staffs working under him generally agreed that the campaign’s casualties would be proportionately small (275,000 men according to Halder), the strain of combat on ammunition and fuel would be low after the first weeks, and the political system of the Soviet Union would be unable to handle such rapid defeats. Even before the air war over Britain was decided, the promise of swift and easy conquest of the Soviet Union proved too difficult to resist.

War with the Soviet Union began to be seriously discussed a month after France signed its armistice. General Fritz Halder, Chief of the General Staff of the Army, noted in his diary that on 22 July, 1940 Hitler made his intention to conquer and subjugate the Soviet Union clear to all his commanders; the day before had ordered the Commander in Chief of the Army, Walther von Brauchitsch, to begin developing plans to invade the Soviet Union. General Erich Marcks was selected to head this initial study.

From its inception the plan was marked by several assumptions and flaws. First, the vast distances of the Soviet Union, while noted, were not properly addressed or prepared for. Second the pervasive racism of German military and political leadership caused them to demean Soviet capabilities, technology, and leadership, leading in turn to the assumption that the war would be short and easy. Third, the rivalry between the two main German military bodies, OKW (Oberkommando der Wehrmacht, High Command of the Armed Forces) and OKH (Oberkommando ders Heeres, High Command of the Army), led to friction, compartmentalization, and competition. The plan was as much about soothing egos and meeting racial expectations as achieving victory.

Marck’s initial concept representing OKH’s view, codenamed Operation Otto, was delivered to Hitler on August 5, 1940 and formed the basis for future variants of what would become Operation Barbarossa. His plan assumed that Moscow would be the campaign’s main objective that the war would last only “9 to 17 weeks”, and most importantly, that the Red Army’s 170 combat ready divisions, an inaccurate number, would be destroyed along the border west of the Dnieper River.

A second study, called the “Lossberg Study”, conducted separately by OKW called for a stronger focus on Ukraine and Leningrad, though Moscow would remain the central objective. It also was more concerned with the flanks of the Ostheer as it advanced into the interior of Russia than OKH's proposal, concerns which would be repeated by Hitler later in the final plan. Though never presented to Hitler, it influenced subsequent planning by Goering and the Reich Ministry of Economics and from there likely reached his ears.

Halder presented OKH’s final plan, codenamed Operation Fritz, to Hitler on December 5, 1940, with the three objectives now being Leningrad, Moscow, and Kiev. The Red Army was assumed to be destroyed within 500 kilometers of the border within the first weeks of war, followed by a pursuit to the Archangelsk-Astrakhan Line.

On December 18, 1940, Hitler issued Fuhrer Directive 21, codenamed Operation Barbarossa, which was a synthesis of the past 3 months' planning. In the final plan the Red Army was still to be destroyed near the border, with the assumption that future reserves could not be raised. Three Army Groups, North, Center, and South, would advance on Leningrad, Moscow, and Kiev, respectively. However, the plan stressed that while Moscow was the most important objective Army Group Center should be diverted to assist Army Groups North and South if they failed to seize their objectives. Rambling and vague, Directive 21 failed to resolve the disputes planning had opened and in fact was a plan only to defeat the Red Army, not the Soviet Union as a whole.

The planning for Operation Barbarossa was marred by a number of problems. Most importantly, logistics and the factor of space were never addressed; Martin Crevald in Supplying War notes that an absurd number of problems were swept under the rug, from fuel consumption to rolling stock. German planners also lacked a unity of command which led to a mixture of objectives and no clear focus. OKH and OKW had each had their own assumptions about what objective would achieve final victory, and forces were diluted along the Northern, Central, and Southern axis to achieve all of them; the Germans entered the campaign with only the vaguest idea of what success meant. Finally, racism towards Slavs caused the Germans to underestimate their opponents and ignore potential problems, maintaining confidence that ultimate victory could be achieved quickly and easily.

German planning for Barbarossa was confused and unrealistic, to the point of absurdity. Thus it's impossible to look at Barbarossa vs Sealion from a rational standpoint as Hitler and his inner circle were driven by irrational assumptions in their decision to go to war. Adam Tooze uses the phrase "mad logic", and I think that best sums it up; Barbarossa seemed like the best option within their own worldview, even if today its flaws are easily apparent to us.

Sources:

Supplying War by Martin van Crevald

Operation Barbarossa and Germany's Defeat in the East by David Stahel

Barbarossa: Planning for Operational Failure by John D. Snively

Operation Barbarossa: Hitler's Invasion of Russia 1941 by David Glantz

The Wehrmacht: History, Myth, Reality by Wolfram Wette

The Strategy of Barbarossa by Austin C. Wedemeyer

Operational Logic and Identifying Soviet Operational Centers of Gravity During Operation Barbarossa, 1941 by Major David J. Bongi

As well as the logistical reasons mentioned here, Hitler kept a favourable view of the "English" (either this is him incorrectly naming them, or emphasising the "Germanicness" of Britain - he often spoke of the "Anglo-Saxons"). He essentially saw them as Germanic equals - this certainly softened the blow when thinking of WWI, as being defeated by an equal is not as hard to accept.

In addition, he had a rather vague plan of Germany ruling the continent and Britain ruling the waves. Hitler even considered offering German troops to help Britain preserve her empire, although to what extent the plan was considered is up for debate.

However, as it became apparent that Britain would not back down, German propaganda had to change to attempt to display the British as evil, Jew-ridden, and everything else you would expect. Nevertheless, Hitler still liked the British and whilst it would be naive to suggest he did not want an invasion, between attacking the "racially inferior" USSR and their "British brothers," Hitler was more inclined to put effort into combating the actual military threat - Britain was not exactly in a great position at the time.

"The Germanic Isle: Nazi Perceptions of Britain" by Gerwin Strobl is a good book on this, as well as Mein Kampf if you can get through it.

There's some evidence to suggest that in Hitler's mind he envisioned Europe as having Germany as a dominant power, but not the sole power, and the British would be more a rival.

Practically speaking though, while the British as a land presence at the onset of WW2 was a joke- their tanks designed from WW1 standards that either had them as a replacement for traditional cavalry, or as infantry support vehicles, their small arms were dated, and many in the volunteer army recounted that there might have been 20 soldiers, a single ww1 field gun and some rifles to protect a mile or two of coast line- to their credit the British possessed a highly capable navy- if lacking for submarines- and a skilled air force.

Germany meanwhile had a navy- kriegsmarine- that was no where near it's intended production figures laid out in Plan Z. At one point Hitler considered simply scrapping the entire above-water fleet. Submarines were useful, but limiting in scope.

And while Germany's air force had plenty of talent behind it, it did lack a few critical pieces of technology. For some bizarre reason the Germans never really developed external drop tanks for fuel to expand the range of their aircraft, and the wizardry of the Supercharger (no pun intended- the Rolls Royce Merlin Engine by some estimates saved England) wasn't something the Germans were not entirely thinking of.

To be blunt, while Germany had many individual technologies that could have made invading the British Isles a reality, in execution the Germans simply had nothing in full production. They had large gliders and naval vessles, but nothing that could be used practically in an amphibious assault. Before Germany could land in England they'd need to establish naval power, which their submarines weren't quite capable of, and their above-water fleet simply could not do. Furthermore the Luftwaffe tore itself to ribbons trying to wrest the skies from the RAF. Granted, the English were doing the same, but they had the advantage of defense.

Similarly, Hitler seems to have sorely underestimated the Soviet Union's will to fight. In both situations he'd hoped that a sufficiently large display of force would cause the states to sue for peace.

My understanding is that Nazi officials were quite convinced that the citizens to the East would welcome them. Did they have such beliefs about the English? What about the other nationalities of the UK? Might this have played a factor in the decision?

There's evidence Hitler wanted peace and preferably cooperation with England. He considered them fellow Aryans (which they are).