No not at all! For one thing the great thing about Britain is that unless you say you're not British, no-one will realise
and then when they find out, they won't care. In my personal experience, the only thing that puts off home students from befriending internationals is either the language barrier (but the majority of people that I know don't have a problem with that) or that it's hard to meet one international without taking a dive into a massive clique...
With mainland Chinese students, a lot hang around in large Mandarin-speaking groups so it's hard for a home student to get chatting to them. If they however join a society that's not just a mainland Chinese social society, then everyone will treat them as they would anyone else.
I met one Malaysian girl on a train back to my university, and what I found sad was that she said that I was the first home student she'd spoken to... she was put in halls with internationals from Australia and the US so she was with other English speaking people but she found it hard to break into the 'home' crowd. I recommended her to come along to one of my society socials, or to any society social. She found the drinking culture a bit bizarre, but you don't have to drink to be part of that culture, although a lot of socials do take place in pubs/bars so you have to be prepared to be around it.
Just get stuck into university life, chat to coursemates, join loads of societies, speak to people in your halls/accommodation and you'll end up with a wonderfully diverse group of friends.