if the hole / tunnel is smaller than 1" I'd go rat, mouse[wood field or less likely house], vole or as an outsider a shrew.
hedgehogs tend to need 3-4" to get through.

hope this helps.

rats leave evidance as they cant control there bladder or there bowl so you will see there droppings . seams a bit late for hedgehogs to hybernate . what sea burn sais is true to . if a rat can get its head in the rest will follow .

We discovered loads of rat runs in our compost in our last garden, and the tunnels were about 2"-3" in diameter. Hedgehogs don't really burrow in the same way - they just push stuff aside, and Nosey's right, it is a bit late for them to be going into or coming out of hibernation at this time of year. What do you intend to do if you decide it IS a rat, Penny?

I first noticed this several weeks ago so it's not that the local wildlife is particularly slow off the mark.........just the gardener! The hole is a good fist sized. And what am I going to do if it's rats? Scream for my husband probably.

It really does sound like rats, especially if there are several runs. I'm dying to know, who is your husband going to scream for? ;o)
I suggest you call in the professionals. These days it costs a little bit, but they'll be able to tell you definitely what your little friends are, and should be able to wipe out any infestation quickly, decisively and (I hope) humanely, without endangering any garden friends. Do let us know how you get on.

if you want to do the deed yourself get the traps that kill them instantly ie like big mouse traps but use peanut butter not cheese as thats an old wives tail as they say . id say rat run as there such opertunists that they will get up in the winter for an opertunity .

It would worry me that the traps (or poison) would kill something other than rats!

We couldn't use poison as apart from anything else we have a very greedy retriever who'd eat anything. However, having enticed husband down garden to view hole, he is adamant that the hole is empty......... The whole compost area needs a bit of a tidy up, so, rmed with a spade, wellies and a piercing scream, I shall go and see what happens.....just as soon as it stops raining!

Aah! But something still MADE that hole, and if the hole is empty, where has that something gone? Good luck with the spade.......

and the scream lol . gattina has a point x .

the culprit may be long gone as it moved on in the autumn.

theres lots of possabillities but if there are know droppings bye now round the entrance its not rats .