I think it will be natural for people who move to a whole different country to be homesick. Bouts of homesickness will happen; IMO, it's unavoidable. I have many friends who have moved to different countries (not just UK/US, but all over the world) - and all of them get homesick every once in a while. I think the people who can move to a whole new country and never feel homesick are few and far in between.
I love living here (been here about 8 months), and I'm absolutely glad I made the move. But I still get homesick - and sometimes really badly. But not bad enough that I hate the UK and want to leave. Overall, I love my life here and wouldn't trade it for anything. But I still miss my friends and family in the US.
A friend of mine (back in the US) lived in the UK for a few years while she was doing her degree at a UK university. She was homesick and missed the US and her friends and family, but it was to a point where she hated the UK and counted down every second until she could go back to the US when her degree course was finished.
So, I guess what I'm trying to say is that you can be homesick, but still be glad you made the move, and still like the UK. Conversely, you could hate it. But you won't really know until you try.
IMO, it's really difficult to predict how you react until you actually do it, but the good thing is that it's not something that will be permanent. If you move somewhere and end up hating it, it's not like you've committed the rest of your life to that location... you can always move back if need be.
Edited to correct some spelling.