You can use your British passport, but it'll make no difference to the bucket you're selected from unless you have a U.K address to go with it, and you have to use the address where you reside. This being said, depending on the uni and the course you want to study, you do sometimes have a greater chance of getting in when applying from abroad because your International fees are more than welcomed. If you look at each school's web site for the subject that interests you it may give a breakdown of the number of places available for home and international applicants which will enable you to apply strategically.