Yes unfortunately we have had lots of damage here…
First squirrels had all our unripe strawberries, then voles and mice ate a whole row (5m) of beetroot before i realised what was happening! Then when I cleared the beetroot they moved onto some squash nearby, nibbling the skins of kuri, So I had to snaptrap them, about 6 or 7 voles and mice, and now no more damage to squash.
And now the worst, rats have eaten about 15 kuri squash in a different part of he garden, when the leaves died down i realised some were nibbled and holed and had been hollowed out from the inside! On a night patrol I saw a family of rats quite unafraid of me nibbling away! They ate them very quickly indeed! Rats have also been nibbling carrots and french beans,
and now my winter beetroot is under attack, again snaptraps set, they have been tripped but no catches, which indicates rats again,
Problem with rats is they are difficult to trap as they are clever, you have earn their trust with food and unset traps, then set them, Poisoning is another option but not eco friendly as posion would find its way into the food chain.
Last year I lost some raddichios to voles and some beetroot but not this much! My friend nearby in Devon has also lost all his beetroot this year.
As for no dig, I’m not sure if that is a factor, we have many moles , drawn to the abundance of worms, and i think voles do share their tunnels a bit. But our garden is quite wild at the edges, being in a woodland clearing, so many places for rats to hide. And voles love our grassy banks, making many runs and homes. We do have a family of tawny owls on night patrol every night 
but i think this year they have their fill and still rodents to spare!