"In Dr. Oppenheimer’s reconstruction of events, the principal ancestors of today’s British and Irish populations arrived from Spain about 16,000 years ago, speaking a language related to Basque."
This dovetails nicely with the Milesian Legends, but the timeframe appears to be off considerably.
The time frame seems to be the most unclear part of this study. What seems certain is that the settlers were in the British Isles before the land bridges submerged around 10,000 to 8,500 years ago.