It's not common as an undergraduate course. I think most going into PhD programmes in bioinformatics will have a first degree in maths or CS, although I don't think physics or engineering are that uncommon. Biology grads who have a very strong quantitative background in their course (typically by taking optional modules in maths or CS I would imagine) might also be suitable, or if the programme specifically has a track for those from a bioscience background. I get the impression most programmes think it's easier to teach the relevant biology to someone with a strong numerate background than vice versa.
"Prestige" of A-level choices is meaningless. If neither chemistry nor CS are required for the course, then the better option is the one you can get the highest grade in. That said, CS would be more relevant for a bioinformatics course, but very few CS courses (and undoubtedly the handful of bioinformatics undergraduate courses) require A-level CS. Normally A-level Maths is the only requirement, although for some courses A-level FM might be useful.
As long as you take A-level Maths any other A-levels are fine, just pick those you find most interesting and/or think you'll do well in. Obviously Biology/Maths/CS (and/or FM) would probably be as close to that course as you can get in your options now. Bear in mind that bioinformatics doesn't actually have a great deal of biology, and is mainly CS applied to biological issues. However, taking A-level Chemistry alongside A-level Biology would still satisfy any programmes in that realm, but would offer you a lot more flexibility if you decide to go down a different route.