The first great known migrations into the UK were the Belgae, a Celtic people, who displaced the Iron Age natives, this was of course well before the concept of the Nation State. The next three great migrations, we’re in turn the Romans, Saxons, and Vikings, all of whom arrived as violent conquerors. We of course don’t know if they were indeed welcomed but as conquest usually involves mass murder,
grape, and confiscation of land it is perhaps unlikely. The next great wave came in 1066 with the Normans. Which resulted in the Harrowing of the North and economic devastation which latest decades. Again unlikely to be welcomed.
Following from 1066 there have been no successful military invasions of the UK. There were a number of Flemings arrived from the Low Countries in the Plantagenet period, who were moved to Wales, again probably not welcomed by the locals they displaced. Roma have been present for centuries, but even today are not universally welcomed, and there have been Jewish communities since the Middle Ages, subject to regular pogrom, which is one of Britains less than glorious inventions.
Anyhow a good potted history here.
en.wikipedia.org
Plenty of secondary sources listed there if you don’t trust wiki. But it is largely correct.
Tell me. Which of these major migrations were welcomed? And note the massive completely out of proportion increase in the last 100 years.