You're not wrong. Where I grew up we had a large Greek Cypriot, Italian and Maltese community from the 1950s onwards. They all had their own businesses, married local women, spoke the language, invested in the community and their children, grandchildren and great grandchildren are indistinguishable from the locals.
In the early 2000s the floodgates opened and the area was flooded with eastern Europeans, Portuguese, Kosovans, Albanians and Romanians. Some of them were ok, but the difference between them and the 1950s immigrants was palpable and the tensions are still there.
I think that demonstrates that the British people are welcoming and ready to embrace outsiders who work hard and integrate into the local fabric of society. It's totally on the incomers to do this and if they don't then they can't complain when tensions subsequently arise.