I looked it up and by some interpretations you are right.
Apparently the first humans in Britain were the Neanderthals, about 900,000 years ago, and all peoples of European extraction have some Neanderthal ancestors and genes. However humans were in and out of what is today the British Isles depending on ice and climate.
Modern humans arrived, when Britain again became inhabitable, after the last ice age, as you say about 12,000 BC, give or take a few thousand years.
https://en.wikipedia.org/wiki/Prehistoric_Britain Roughly the same time as the first humans, our Native American's ancestors, got to the Americas.