I know about your legal rights but I am fairly sure that the timing belt is something that would be expected to wear down and I thought it was every 40-60k miles (although you are under that mileage to be fair).
I take it you have had the car from new? Has the belt snapping caused any other damage? I have heard that belts cost around £90 plus fitting obviously.
I do not have mechanical knowledge so someone else can advise on that but on a 6 year old car, I can imagine it being very difficult indeed to force a repair under the Sale of Goods Act.