Welcome to The Answerbank.
At a guess, your cheque will simply sit in their "What the hell do we do with this?" pile until you contact them to get your problem rectified. (Realistically, there's not much else that they could do with it, is there?).
Have a word with the counter staff at the Post Office branch where you paid the cheque in. I'm sure that you won't be the first person with such a problem, so there must be a solution to it.
(Just for future reference though: If you've got a smartphone, and put your bank's app onto it, you can probably pay in cheques simply by photographing them. You definitely can with the Barclays app, anyway).