What is your position? Have you found somewhere, is there a chain?
Is this £10k on a £100k house, or a £500k house?
I would work on the assumption that best case, your FTB will drop their offer by £5k when the survey comes back. Worst case, they'll pull out and you'll lose your house.
We came within a whisker of this happening to us when the FTB was wrongly convinced we had subsidence - because he had done a search on the planning site for the local council for 'Acacia Road' and found an application to repair subsidence, where as we were 'Acacia Street', nearby. At this point, if someone had said I could pay £5k to make it all go away, I would have done, even though it would have made things tight for buy the new place.
It all worked out ok in the end, but we had a few sleepness nights.
Oh, and his parents were putting up the deposit, so they wanted to come and do additional viewings and their own checks on things, so be wary if they are in that position as well..!