However, the British Isles got majorly-separated from Europe about that time.
Yup. My grandmother Mrs Smith's people (Dad's Mom) in Scotland and Finland, haplogroup U5a1a, were seperated by this event. Previously they could walk across (What is now the North Sea) for a visit.
BTW, Cheddar Man was/is haplogroup U5a too.
I think making a causal connection is a real stretch. The world was getting warmer, growing seasons were longer, glaciers were retreating. Sounds as though it was a good time to start agriculture.
There can be no exact timing on events that far in the past.
And if the Black Sea Flooded as a result, wouldn't the final effect on sea level be just about all even?