Simple. according to the BBC
http://www.bbc.co.uk/history/ancient/british_prehistory/overview_british_prehistory_01.shtml
Over the millennia there were phases of extreme cold, when large areas of Britain were covered in ice, followed by warmer times. Around 10,000 years ago, the latest ice age came to an end. Sea levels rose as the ice sheets melted, and Britain became separated from the European mainland shortly before 6000 BC. (6000BC! I guess chief was talking about some Island other than England. Maybe atlantis, Greenland or something else… but the english isle.)
The people living on the new islands of Britain were descendants of the first modern humans, or Homo sapiens, who arrived in northern Europe around 30,000 - 40,000 years ago.