First of all a big hello! Welcome to the group.
My husband did Bunac, but the other way. (Went from the UK to USA) so if you have any questions, I may be able to find out for you.
As for renting flats here, first be aware that flats in London are very expensive. If you are coming over as a student, you may want to think about finding a flat-share and living with another couple or another person. This seems to be very common here. We lived in a place with three other guys for the first few months of our marriage so it can be done! For this type of arrangment, I expect Bunac webpages may be very helpful.
However, if you're going at it on your own, my advice is to definately wait till you get over here. The process is very different, and finding areas where you want to live can be tricky. (There isn't any 'avoid the east side of town' sort of thing here....neighborhoods vary greatly street by street.)
Plus, you'll have to go through a letting agent and you won't find any that will work with you before you get here or more than a couple of weeks before you move. It's a fast market.
Anyway, hope that helps ans congrats on your upcoming graduation!
Let us know if we can help with anything else!!