Is the British invasion called that in the UK?

I’m not sure what you’re referring to. Could it possibly be the Revolution when Americans earned their independence? I can’t think of much that we particularly invaded and took over, apart from small ports in order to trade with the rest of the country, though we did keep a bit of it for ourselves. Most people didn’t know that it was happening owing to the communication technology available at the time. Others might mishear the term and use it for when the English invaded Wales and Scotland, though they’d refer to the invaders as English rather than British. Some people seem to think it happened when the Beatles came to America, but all they wanted to do is play a few records. So can I think the same way when Trump pops over to play golf? But if you take the intelligence of some people, it could be the sale of Cadbury bars for all they know. Sometimes a bit of context is good.