The British Isles have been inhabited since the end of the last Ice Age - about 10000 years ago. The Romans occupied Britain hundreds of years before the Anglo-Saxons who didn't arrive in Britain...
A date of roughly 450 AD is widely accepted as the time of the first major influx of Angles and Saxons. Of course they didn't all arrive at the same time. For example, around 400 AD there were enough...
Initially people known as Angles, Saxons and Jutes were employed as mercenaries to help fight the raiding parties of Picts, Scots and Irish, but they liked the place so much they brought over more...