Personally, I think that Churchill's government would have fallen a few weeks later as the dust from the fall of France settled and the British would have sued for peace if they lost a large majority of the BEF. I will point out that this is an important IF, but I'm playing along with the assumption that this is possible.
Yes, the British had the ability to fight on regardless, but you have to factor in the psychological factors. The miracle of Dunkirk is what gave the British the resolve to continue in face of the disaster in France. These soldiers were also vital for pretty much everything the British did to Germany on land until 1944; without them, there's nobody. Even the core of the Free French would be swept away. Nobody to land in Greece, nobody to reinforce Egypt, nobody to teach the Americans rookies the right end of a gun
Because Churchill chose to fight on in a difficult time, we're a bit blinded by the illusion that the British would have fought on 'no matter what', but the truth is that his government was not invincible, and that while HE would not make peace, there sure as hell were people willing to compromise.
Amusingly, given Hitler was already thinking about invading the USSR while the ink was drying on the armistice, you might actually see a logisitically-nightmarish attempt to an invasion of the SU in August in this scenario, where the Germans would be trying to move the whole army back to Poland in under 3 weeks to face an even-more-incompetent and freshly-purged Red army in an autumn campaign. His generals had to talk him down from the notion of a campaign starting tentatively on July 31st in OTL, insisting on the logistical impossibility to be ready for it before September. Even though he justified his invasion with the need to defeat Britain's only hope in OTL, something tells me if you take Britain out, he'll be even more convinced about how invincible his army is and do something stupid.