Are you certain its foxes? They don't usually dig up lawns or borders unless they're making a den.

Ermmmmm sprinkling Human Urine around the perimiter is supposed to deter them!!

I've found that foxes and badgers dig up grass in winter, but by this time they're a lot less desperate and stop doing it.

badgers normaly do it for the worms which is a big part of there diet . another idea is to put human hair in old tites or stockings and hang them round your garden .

I'm wondering if its birds getting at either leatherjackets or chafer grub...

it could even be hedgehogs . its a pity you cant stay up one night and find the culprit .