What you have to ask yourself is will you be happy at Exeter? If your answer is simply no, or you have a massive hesitation, then it may be worthwhile sitting out a year and reapplying. Look into what those other unis have as their entry requirements if you were to reapply. It's completely your call!
Further advice - as for Exeter, it's a very renowned university if reputation is a big sticking point. Also, you would have to consider what you would do in that year off, which would essentially be a gap year. Whatever you get up to, whether that be a job or travelling (or something else entirely), would it enhance your personal statment next time round. As I say, it's your call and nobody else can make that decision. Whatever you decide, make sure you're happy.