Not true. Until relatively recently, Britain only had very small numbers of non-whites. Look up census reports throughout the 20th century or even footage of London (where British people are now a minority) from as recently as the 1970s, you will see it was still mainly white people. It didn't look like Nigeria and Somalia mashed with Pakistan and Saudi Arabia.
The demographic change accelerated after 1997 when New Labour opened the floodgates to the third world and annual immigration increased to the six figures.
If you're referring to the ancient invasions by Romans, Normans, Vikings, etc. They were fellow Europeans, not Subsaharan Africans and Asians, and they also left very little genetic trace in Britain, anyway. The only invaders who left a sizable genetic trace were the Anglo Saxons. The population of the British Isles was virtually all indigenous until quite recently, especially in the Celtic peripheries.