You're probably right about card payment being a condition of the contract, but a contract has to be enforced by a court: the police, if they turned up, would shrug their shoulders and say it's a civil dispute. In the somewhat unlikely event of an English court being willing to accept the case and take it seriously, I would guess it would probably order that the diner pay the bill (which they could now do in cash because it is now a debt and I'm assuming traditional legal tender rules still apply), and that the restaurant pay the (probably much larger) court costs because, seeing as the diner had already offered to pay the bill in cash, the restaurant is clearly to blame for the matter coming to court and everyone's time getting wasted. The restaurant might also have to pay the diner's legal costs, if there were any, if the diner made a good impression of not having deliberately caused trouble.