As conditions improved hunter/gatherers could move away from the Western European refugia Northern Spain, just south of the mountains.
One of the first groups to leave are now believed to be the people we know as the Sa'ami. They moved due North up the coast, and crossed to America, and went South into North Africa, and in time, managed to leave behind their marker gene sequence among the Sakha/Yakuts (ancestral to the Japanese ruling clique who invaded in 560 AD and imposed Buddhism).
It's possible they took along a Welshman or two, but they'd had to have left the Refugia first.
I wonder what the climate was in the hilly country in Wales at that time. Might have been inopportune to bother settling there, and with few people in Western Europe, they couldn't go everywhere.
Also, there's this thing about the Younger Dryas popping up and ruining everything. Evidence is a residual population of Sa'ami actually "wintered over" 1500 years on the Arctic coast. At the same time, their cousins in America were pretty much wiped out.
That climate anomaly definitely kept Britain miserable until about 9500 years ago.
Those people were some tough mugs. Can you imagine surviving by hand-building small wooden kayaks and traveling along the ice for months at a time, living on seals and fish, and sleeping in the open ocean in sub-freezing temperatures? My wife uses 3 blankets if it drops below 70 in the house.