Yes, the plan was, after assuming air and naval superiority, to begin an amphibious invasion of Britain codenamed 'Operation Sea Lion'.

However, it is quite debatable that the German Kriegsmarine (Navy) would have been able to overcome the British Home Fleet (which was numerically far superior) even with air support. The pre-emptive scuttling and destruction of the French fleet by Britain also ensured that the Germans would be unable to utilise France's fleet either (if that hadn't had happened, then even the British Home Fleet could have been overwhelmed).

Another problem was the lack of German landing craft. The Kriegsmarine had very little time to assemble an invasion fleet on the scale required to invade the Isles, so they opted to convert river barges into rudimentary landing craft. These would have been easy pickings for the Royal Navy, and would have greatly limited the amount and type of artillery the Germans could bring with them.

We can conclude safely that Sea Lion could have succeeded in its initial phases with a stronger German Navy, however the loss of the Battle of Britain ensured such an invasion would be extremely risky, let alone lead to actually controlling Britain with any significant force.

However, if the hypothetical invasion had taken place and succeeded, there appear to have been plans to have divided the United Kingdom and Ireland into six different administrative areas, headquartered in London, Birmingham, Liverpool, Glasgow, Newcastle and Dublin. The Nazis intended to return Edward VIII to the monarchy, as he had perceived sympathies to the Nazi Government, as indicated by his visits to the country in 1937 (the British Home Office maintained that he has remained completely loyal to Britain throughout the war).

Mark Mazower in Hitler's Empire asserts that the Germans would likely have split Scotland from the UK, and formed a United Ireland, all in an effort for German hegemony over Western Europe. Some of the more shocking aspects of such an invasion were revealed from captured from German war documents. The Nazi Commander-in-Chief directed that the able-bodied male population would have been deported and interned (see: slave labour) on the Continent. The UK would then have been plundered for anything of value, and the remaining population ruled over tyrannically.

Alison Brooks, "Why Sealion is Not an Option for Hitler to Win the War", is a pretty devastating takedown of "Operation Sea Lion". She coined the term "Alien Space Bats". On Sealion, she wrote "Personally, I think alien space bats are more plausible". (Or that Alien Space Bats would be the only force that could get the Confederacy a win in the US Civil War, et cetera.)

"The Luftwaffe, with its resources, was expected to do all of the following:

• Act as artillery for the landing forces
• Keep the RN out of the Channel
• Win total air superiority
• Prevent British Army reinforcements from getting to the zone by bombing railway lines
• Make a mass attack on London to force the population to flee the city and choke the surrounding roads.".

In reality, they managed none of that. In any event, the RAF wouldn't have been wiped out before the invasion. "Dowding had made preparations to pull 11 Fighter Group back to the Midlands in order to preserve an effective fighter opposition to an invasion proper."

Even if you wave away the RAF, the Royal Navy still had massive naval superiority and the Luftwaffe was poor against them, the German transport and resupply plans were pathetic, the operation was on far too broad a front, no plans were made for artillery (Luftwaffe, supra.), there's the Military Canal and the Germans had no plans to bring bridging equipment, hostility between the German army and navy was causing large amounts of friction in planning, ...

It ends, "We can choose to wave a magic wand, and wipe out the RN and the RAF, and examine how successful the invasion was likely to be in their absence. Sandhurst has done this on four occasions to my knowledge. Both sides were given the historical starting positions, with an invasion date of 24 September.

"In each case, the details of the fighting varied, but by each analysis resulted in 27 September dawning with the Wehrmacht holding two isolated beachheads, one at roughly 2 divisions strength on Romney March, and one of 1 division at Pevensey. Each were opposed by more numerous forces, with growing numbers of tanks and artillery. German resupply was still across open beaches.

"Operation Sealion can only be described as a blueprint for a German disaster."

So let me piggyback a question...

Germany rules the skies but can't invade. What do the countries do now? Does UK hunker down and wait to strike back? Does Germany use daily bombing to force a change in government to one willing to sign a truce? Would a truce even be in Germany's best interest?