I think the trouble with that, as presented CastleFarm, is what constitutes 'incomers' and what's 'British'?
Angles, Celts, Saxons, Normans, Vikings........?
You get the drift. To fix society at a particular point in time and say 'then it was British, these 'new' people aren't' is both flawed and divisive and just has folk hating each other, which is a waste of energy, amongst much else.
The trick is for us, all together in Britain, to decide what we want. And then insist everyone abides by that. Rather than having one set of rules for one group, another for a different group. That's what gets people cross.
Britons are pretty tolerant, which is great. When that morphs into 'we really mustn't upset anyone so we won't ever discuss or challenge anything', well IMHO not so great.