Exeter, as a city, isn't very diverse - the South West as a whole is predominantly quite rural and has very few people from ethnic minorities. The University is rather better, and the increasing numbers of international students at the University mean that the character of the city is changing gradually and the population is becoming more ethnically diverse. And, yes, there are British students from a variety of ethnic backgrounds, too - but it's fair to say that as a city, Exeter is predominantly white.
I was born in West London and I still find it odd not to see a mixture of different people, but it's much, much better than it was when I first came here. You certainly wouldn't be the only non-white person around, but you'd be in more of a minority than you would in a big city, and it's fair enough that you want to take that into account when deciding where to go.
It would be easy for me to say that people from all backgrounds should come here as that would help to make it a more diverse city - and that is what's increasingly happening - but since I'm white it would also be rather naive of me to assume that you'd be comfortable doing that. The best advice I can give is, come and see for yourself. Have a look round the city and the campus, and see whether you feel comfortable. Only you'll know what will work for you.