Only Commius fled to Britain to escape Caesar and only his tribe - the Atrebates - have the same name as a Belgic tribe. Presumably the Belgae conquered this part of Britain and ruled over it, enabling him to escape there, like the Portuguese government relocating to Brazil to escape Napoleon much later. Diviacus of the Suessiones is supposed to have been the man who started Belgic involvement in Britain c.100 BC but how large an area he conquered we don't really know because it's hard to decide on the exact significance of the archaeology, whether it was just the Atrebatic corner or whether that was all that was left of what had been a Belgic "empire" in Britain.