JAVMan
I'd get advice on this, I think that you are in a strong legal position
We once had a bespoke holiday booked, we realised that they had missed out some elements, they tried to get more money out of us after the deposit was paid. Saying exactly the same thing as you, "pay more or cancel"
We spoke to citizens advice, they said that as it is a signed contract, the problem is with the dealer, YOU should not cancel, if the dealer chooses to cancel. You need to advise them that you can pursue them for a "loss of bargain claim". Which means that if you have to pay more elsewhere, they would have to fund the difference
The key thing is that you do not cancel and you tell them that you do not accept the change to contract. Advise them that if they cancel and your resulting order costs more, then you will raise a loss of bargain claim
Edit - that was about 18 years ago, worth checking if that advice is still valid