I am interested in Both Maths and Physics, but I would defiantly consider myself a Mathematician before a physicist.
I felt the same way before university, I ended up doing Theoretical Physics, as I was worried that if I did joint Math-physics I would miss out on a lot of essential physics. However now having finished uni I feel like its the other way round, and that I took lots of unessential things to what I'm truly interested in (labs and some other courses that are more applied physicy), and I wish I had the chance to take more formal courses in things like Differential geometry/Group Theory/Algebraic Geometry/Topology, so I would prob choose joint math-phys if I could turn back the clock.
I guess this only really is the case because I am hoping to go into String theory/High Energy Particle physics and I almost feel like so many courses I've taken are of no use to me now, whereas formal maths lectures would have smoothed the way so much. Don't get me wrong it's possible to learn the physics without being a maths undergrad, e.g. If you go on to study General Rel then they'll give you some preparatory lectures on Differential geometry, but it can be a little unsatisfying, because you feel like you only have a vague crumbling understanding of the very thing underpinning the whole subject.
Of course it really depends on what your ultimate interests are, for example if you're going to be interested in any branch of physics other than String theory/Quantum Gravity/Elementary Particle...then the choice is prob do straight physics...if any of these areas do joint Math-Phys and make your life in a few years a bit easier...Then again you may fall in love with Pure Mathematics and want to do something like Number theory and forget all about physics...
I guess the clear choice is do Joint MathPhys...although you still may find it hard after year 1 to choose between either subject, since 1) in the first yeear of a straight physics course typically more adv maths is done than in a first year maths course (again because mathematicians are so formal and rigourous so it takes longer to get to the juice) 2) you won't do much exciting physics in year 1 either, just prep things like electromag, thermo...
In the end it doesn't really matter, it just makes your life easier later, the sooner you decide what you ultimatley want to do...
As for Bristol/Warwick, I have no idea :)