Probably slugs, go out after dark and take a look. Try beer traps, dry sand around the plants, crushed eggshells or any other shells. They like to hide under the plant pot saucers so leave these about and check and remove any slugs in the day and at night. Put them in the bin they'll be happy there!
Thanks johnk and ruthandsam. I think the vine weevil larvae may well be the culprit as it is definitely the roots that are being attacked. Will have to see what the garden centre has to offer.