Given that you only bought the van last week, the seller is well within their rights to offer you a full refund instead of a repair. I imagine that the dealer is worried that there are other issues with the van and therefore wants to avoid a series of costly repairs. Unless you can prove that the seller promised to replace the cam belt and water pump prior to you collecting the vehicle, you’ll struggle to legally claim the money back for the work you’ve had done by another garage.

You could try and come to an agreement with the seller in regards to a part refund to pay for the gearbox repair. However, given the money involved, I suspect that the dealer simply wants to take the van back in order to fix it at the lowest possible cost or to get rid of it at auction. I'd push for a settlement where the dealer provides some goodwill payment towards the work you've had done. Tell them you will agree to a full refund, but only if they pay some (or all) of the cam belt costs. If they're desperate to get this van back, they might pay this just to settle the matter. For your legal rights, see: www.honestjohn.co.uk/faq/consumer-rights/