DNA analysis of men in England and Wales shows that a lot of them share a DNA marker that is very common in Italy. This phenomenon doesn't appear in the DNA of men in Scotland or Ireland. It is theorized that the cause is those very active Roman soldiers in Britain from 43-410 CE, who seem to have spread their DNA around with lasting effects. The Roman army mainly occupied what is now England & Wales, and stayed out of Scotland (pace Agricola) and Ireland ("We don't want the Irish!"--Blazing Saddles).
I don't know about the math that brought us to "one million Brits."