The situation on June 22 (the date that France surrendered to Germany), according to the official history of the Canadian Army:
So far as the Army was concerned, it might have seemed that the situation on the day of the Franco-German armistice could not have been much worse. Equipment-or rather, lack of equipment-was the crux of it. The forces in the United Kingdom were "almost unarmed except for rifles"-and there was, indeed, a serious shortage even of them. "There were . . . hardly five hundred field guns of any sort and hardly two hundred medium or heavy tanks in the whole country". It would be long before British factories could replace even the material left in France. Canadian industrial capacity, of which the British Government had been unwilling to make large use before Dunkirk, suddenly became important in British eyes; but many months-even years-would have to pass before the orders for equipment now belatedly placed could produce results. Canada, we have seen, was ready to send what help she could from her reserve stores, but because her pre-war forces and preparations had been so small, she had little to send. Thanks to their low state of preparedness, indeed, "None of the British Dominions", as Sir Winston Churchill bluntly phrases it, "could send decisive aid". The United States had large reserves, and in the new state of mind which the crisis in Europe had produced the American government and people were quite willing to send these to Britain; but getting them there took time.
On 18 June, by which date nearly all British troops had been evacuated from France, there were in Great Britain and Northern Ireland a total of 28 field divisions plus 15 independent brigades of various sorts. These rather imposing figures, however, give a misleading impression. Almost all of the divisions were either recovering from Dunkirk or still incompletely trained; and almost all were without heavy equipment. Of the British divisions, the most advanced were the 3rd, which as already noted had been re-equipped with a view to being sent back to France, and the 43rd; but even these cannot have been in very efficient condition. The strength of the 3rd on 6 June, following its return from Dunkirk, had been recorded as only 4500 men; and the 43rd was reported, at the same period, as "rather backward" in training and equipment. The 52nd (Lowland) Division, we have seen, had got to France and had been withdrawn, but it had left a "considerable" part of its transport behind it. It was accordingly not in condition to move and fight.
No argument from me on the difficulties of getting German troops ashore, but if through some miracle they did manage to land, the British were severely disadvantaged, and other history being a guide, not outside the realm of possibility to think a puppet government could have been put in place. Anyway, all this is in reaction to the notion that a defeated England would today be "speaking German" in the astonishing event of a German victory. They wouldn't.