I feel like I have a black hole of knowledge in WW2. The way I was always taught plus what I later picked up on my own was, the Battle of Britain wasn't ever really going to get Germany anywhere, but they fought it anyway, and lost pretty comprehensively (even if neither side fully appreciated it at the time). This was ~75% of the way through 1940.
About halfway through 1941, Germany launches Operation Barbarossa, which ultimately completely changes the trajectory of the war. But between those two periods, there's about nine months which was basically never accounted for in any class I ever took, nor ever saw anything about. I know Germany mucked around in Greece and the Balkans for a short stint bit because Italy was woefully unready for war from the getgo, and I assume they were generally preparing for the invasion of the Soviet Union in some indeterminate fashion.
But absent in that summary is what was the UK doing? At this point in WW2, they must know they basically have the Isles secured, and they had already rejected peace at least at that stage. So their only remaining needed goal is to figure out some scheme to actually, actively defeat Germany. But I have no idea what their plan was? What was their thinking? What were they trying to do at that point?
Part 1
There are two distinct aspects to this question and im not sure which you are predominantly referring to; what was Britain (and presumably other allies and dominions) doing between the fall of France and the invasion of the Soviet Union, and what was the British (and its allies) strategic plans for victory against Germany and Italy. These are obviously not necessarily the same. But actually I think they do show an interesting degree of similarity that arguably illustrates Britain’s strategic direction: Secure immediate safety, secure global lines of communication, control enemy activities outside Europe and try to bottle them up. Wait. And hope that future developments will favour you.
Many of the things you mention “Germany mucked about around Greece and the Balkans” of course had profound effects on British strategy and activities. British military deployments owed as much to reacting to developments as to executing their own plans and strategy. I don’t think its unfair statement to suggest that practically Britain was reacting to events. And it was VERY BUSY.
Sink the navy of your recent ally? Check. Fight a defensive air war? Check. Surprise naval attacks? Check. Fight in West, North and East Africa? Yup. Greece? Yup. Iraq? Syria? Why not.
There were a lot of these events; those 9 months are jammed with events that involved British and allied involvement. Probably too many to go through in any detail greater than you might pick up off wikipedia.
As for general Grand Strategic approach, Britain had, with varying consistency, advocated and followed a broad concept of ‘Long War’ since long before the outbreak of the conflict. Relying on economic strength and global mobility of resources to grow stronger while slowly strangling Germany of the resources it needed to wage effective war. This idea was neither universally agreed nor followed at the time, and certainly criticised since. This approach had obviously been disastrously affected by the loss of France, yet in many ways the concept continued at a much higher tempo with more significant stakes. As frankly there were not any other options. Britain was not going to return to mainland Western Europe any time soon.
Spending was going to need to be higher (unsustainable), mobilisation of the economy greater, militarisation more dramatic, but the goals generally the same. British global power, trade, resource flow and strategic mobility must be maintained. German and Italian strategic options must be bottled up in Europe and its adjacent waters. Blockade and economic warfare must be given time to work, even given the knowledge that these approaches would be harder than ever, perhaps even impossible. Time must elapse to see the fruition of British armament expansion put in place in the late thirties. Large naval construction plans and bomber plans were due to come to fruition by 1942.
Our hindsight of the war, the great army campaigns of the Eastern Front, Overlord and the Western Front, tends to let people overlook the kind of victory Britain (and France) thought they were going to get. It wasn’t going to end with British and French tanks in Berlin. It was going to be more like the first. Popular discontent, mutinies, Army/business coup, surrender/Treaty. As far as Britain was concerned this was going to be via long blockade, economic strong-arming of neutrals and probably strategic bombing.
There was still a sense, or at least hope, that this was still an option. That Britain and its allies would continue to become stronger, and Britain must be seen to be a practical and viable potential ally for an eventual partnership with the United States. Daniel Todman described the general post France approach as favouring the wishful thinking of future US economic benevolence over striking a deal with Germany that may see them losing the Empire. Other historians have inferred that Britain chose long term American domination over German. The eventual inevitable involvement of the United States was an (unofficial) cornerstone of British policy. By Jan 1941 staff talks between US-UK were taking place and it seemed only a matter of time before the war was expanded further, probably including japan, maybe the Soviet Union. Time was still felt to be Britains friend. Even though Britain was now spending its money like there was no tomorrow, there was a hope that the German war economy was a shambles waiting to collapse. Whose economy would break first? Churchill certainly hoped that the US would literally bail them out if it came to that. Germany had no such fallback. By fighting for lost causes, such as Greece, Britain was in part playing to the global audience, insuring that the US would have to eventually step behind them in one form or another.
But even without any future involvement by the US. Continued British strength was the basis of any future negotiated settlement with its enemies. As the French surrender illustrated, a strong navy and overseas territories was a strong bargaining chip. On top of this was still the hope that war pressure might still see the German economy collapse, leading to regime change. Italy was viewed as a soft target and especially vulnerable to economic warfare and blockade. Italian defeat at sea, colonial defeat, and economic isolation might see a separate Italian peace. Italy’s alliance with Germany counter intuitively was (perhaps optimistically) viewed as route to weaken Germany. Like a weak Austria-Hungary, draining German economic and military resources. An Italian collapse might provoke the kind of Officer/business revolt in Germany.
Massive coordinated bomber offensives were in offing in the next few years. The scale of aerial assaults being envisaged had never been undertaken before and their chances of success therefore difficult to gauge. Again, time was perhaps on Britain’s side. There were wishful hopes for the success of bombing campaigns. Again remember that this vision of victory is not British tanks in Berlin, but domestic and economic collapse sparking soft revolution.
There were no quick routes to British victory but that does not mean that they could not see the possibilities. However, these options still arguably needed the following parameters
Robust and healthy defence of the UK and home waters
Clear lines of communications with Empire, Allies and overseas markets
The bottling up of Germany and Italy (for 2 and 4)
Finding ways of pressuring Germany but especially Italy into surrender.
Woo prospective allies. Especially the US.
And this is really what drove most of the activity in late 1940 and early 1941. To be honest this is what drove Britain for the next few years. Bottling up enemies to allow freedom of movement of military and economic resources. However, much of this, as previously stated, was driven by events, reacting to enemy attacks while trying to bring the strategic rear into line.