Oh, Roy, heartfelt commiserations :'( Been there! We've been growing tatties for many years and virtually never water especially when the weather is hot as it has been believing that it raises the humidity under the foliage and increases the risk of blackleg, blight etc. and anyway the the heavy foliage does help retain the moisture deeper down where the tubers are growing. We could be wrong and the experts may tell you different but can only speak from our own experience.
This year especially we have been having some (very) small doubts as we have large flattened areas where the foxes have been resting and the soil does look very dry and dusty so today Mr W bravely gripped the fork and dug up the first couple of shaws of Lady Christl - absolutely fine, good size and plenty of them - SORRY and really hope that doesn't sound smug but keep fingers crossed for the rest of your crop.
PS just noticed your question - if there are tatties and they aren't rotted then I'm sure they'll be fine - hope you will get better results than you expect, Roy :-*