hi! yes, people have been migrating to Great Britain from the European mainland for a very long time. In fact, it didn't used to be an island -

If the oceans were drained, what would be the top archaeological digs? What would be some of the top salvages? (I'm sure there was a more thorough thread on this, but can't find it)

here are a few posts on the topic of various early inhabitants

Who lived in Britain before the Celts? - the beaker people

What language would have been spoken during the building of Stonehenge?

Who inhabited the British Isles before the Roman invasion? - Celts

What made the Angles, Saxons and Jutes decide to leave their homelands and settle in Britain? - Angles, Saxons, Jutes

How integrated were the Saxon and Viking communities in 10th-11th Century England? - Danes

... and then the Norman invasion