As people have said, any attempt by Germany to invade Britain would fail. The Royal Navy alone was an impenetrable wall, even without air power.
That said, losing the BEF would be devastating for Britain. Dunkirk was the silver lining in a year full of disasters, and allowed the British to keep up morale despite now being alone in Europe against the Axis (not alone globally of course, the Empire/Commonwealth were supporting).
Without Dunkirk that morale might not have been quite so unshakeable, as a large number of fathers, mothers, and sisters would be fearful of what was happening to their sons and brothers who are being marched to PoW camps somewhere in Europe.
More to the point, it would cripple Britain’s long-term ability to wage war. In our timeline, Dunkirk saw the BEF return intact, but virtually stripped of all its equipment - few tanks, few artillery, few trucks, all left on the beaches. And there were so few rifles and grenades in the country that for a few months afterward, the Army drilled using props and wooden tanks.
But equipment can be rapidly and cheaply replaced, and replaced they were by the Autumn of 1940. But men? Men are much harder to replace. Losing a third of a million soldiers would take years to overcome, and would mean tough choices between impacting industrial output in favour of men in khaki, as well as having to completely replace all the experience, training and expertise that the small professional volunteer British Army had now lost.
Britain might have opted to continue to fight, but it would be less confident and less effective for much longer, and would have been less effective in taking the fight to the enemy.
One thing that may have happened is that the British may not have had the manpower to hold into Suez, giving Italy access to the oilfields of the Middle East. That may have been a key ingredient to keeping the Germans’ war machine able to crush the Soviets, and start a southern flank via the Caucasus.
So not an immediate collapse of Britain, but it may well have become more of a liability than an asset to the Allies.