The British were able to keep the French Fleet from falling into Germn hands on their own, by taking out a good portion of it at Mers el-Kebir. They rendered roughly half the Italian Fleet unusable at Taranto. Even if the Germans had taken the entire French Fleet intact and convinced the Italians to assist them in invading Britain, the British were doing a good job of eliminating the threat these two navies posed on their own. Then there's the small matter of Britain's aerial superiority and its coastal defences, which were pretty effective. They were even stockpiling poison gas to use in the event of a German invasion. Germany could never have successfully invaded Britain.I still think that the germans could have successfully invaded britain if they had negotiated different armistice terms with Petain's France (hell, let them even keep the damn Alsace-Lorraine). The UK had a defeated army, no heavy material and no defenses to speak off immediately after Dunkirk, but the english channel. If the germans had gotten the french and the italians to join their navies in an attack on the UK, the RN would be unable to keep them off the channel. As for troop transports, the british managed to scrap together a fleet of common ships to evacuate their soldiers from Dunkirk, under bombardment, so why couldn't the germans do the same thing for an attack?