Eaten potatoes

This is something that I never experienced on my allotment in the UK but since being here it's been a recurring problem and, this year, it's the worst it's ever been.
Field voles which tunnel everywhere and just don't stop eating. I lifted my King Edward's today and some plants just had a few marble sized potatoes left. The others were almost completely devoured - tiny pieces of potato left in the ground and loads of teeth marks.
I have Sarpo Mira and Nicola as main crops but have no idea if they actually have any potatoes left under the haulms whiich are still green and leafy. I don't know what to do? I have a cat that is a great hunter but the damage continues. They also eat carrots, beetroots, chard (the roots), parsley and even leeks. Any ideas or experience welcome.