Meloncollie, could it be something other than voles or mice? Of course they can make holes gardens but I thought the usually went for bulbs rather than roots. Could it be an infestation of crane fly larvae (ie leatherjackets)? They eat grass roots and plant roots and make holes when they emerge at night which birds can make bigger when they search for the. Just a thought given you have so many holes. I once had this problem in my garden in Ireland and had to treat the lawn with some mixture applied with a watering can.