Across Britain's many Neolithic archaeological sites, researchers have extracted DNA and compared it with Neolithic DNA throughout Europe. They were able to determine that the humans inhabiting Britain at the time descended from people in what is now Turkey. There was a great migration in 6000 BC, with people migrating up into Eurasia, and others moving along the Mediterranean. Genetic evidence shows that the Mediterranean group were the British settlers, arriving in 4000 BC. They would have encountered native hunter gatherers on the island, whose population went into steep decline after their arrival. Genetic analysis has shown no mingling between the two groups.
The Neolithic farmers were well equipped to survive in Britain, and quickly outnumbered the hunter gatherers, likely due to agriculture. They are also believed to have introduced the practice of building megaliths such as Stonehenge. However, they were practically wiped out as well in 2450 BC when another migrant group from Europe displaced them.
I find it interesting that there were two big genetic shifts in the population over only a few thousand years. Since Britain is an island, these genetic changes were more drastic. While the Neolithic farmers had brown skin and brown eyes, later immigrants like the Beaker Folk and Anglo-Saxons had paler skin which is now predominant.