I'm old, and I can remember before 1975 quite clearly.
I grew up in Liverpool and we had all sorts of people living there - owning or renting houses - and getting on with their lives. There were enough Norwegians to have their own church. A fair number of Germans, and a Frenchman who ran a well-known cafe (probably lots more I didn't see). We even had Americans, mostly military people but not all. As well as lots of people from the Commonwealth countries, I can remember my first taste of a curry (a chick pea and potato masala on naan bread) and of wonton soup, not to mention cassava chips.
UK mainland is quite large - it does not feel like an island if you know what I mean. There are a lot of pretty diverse communities. Because of our history (ok, maritime power and imperialism) we have been open to most of the world. Most of the male members of my family tree (going back 8 or 9 generations) arrived on boats, most from other parts of the UK but some from other places (the women stayed put - often living in the same house for their whole life). I live in the midlands, quite near a small nondescript field where people think the first (beam) engine was erected - it pumped water out of a coal mine and that is where the industrial revolution began.
If you have skills, there will be a points system and you will get a visa. Just like the US, if you put down roots and want to stay in the UK as your main home, there will be a way of applying for citizenship. Many people here work remotely in a variety of countries where there is no formal 'free movement' agreement and they seem to get on.
PS: Our mountains are a bit crap though. Scotland has some reasonable ones. They call them 'munros'