In thata case, your best bet is to buy a new pair of wheels and then go to a proper old fashioned cobbler who would help with this sort of thing (not Timpsons!).
Is a specialist skate shop what you are looking for? There is still one on the seafront in Worthing (I think) which did repairs to skates so should be able to provide a new wheel or pair of wheels. I would assume there is somewhere similar in Brighton or even Birmingham where you are next weekend.