It's adjacent to the tree stump where the stag beetles used to live before the magpies got them. It could be that the hole was started by magpies to get at the stag beetles or that something bigger saw the carcasses of stag beetles and decided that it wanted a piece of the action. Whatever, it's now an excavation that goes quite some distance underground (it bends away so I can't see how far it extends). It could be an animal's den or perhaps just a route under the hedge (but probably not, as there's no light entering it from another direction).
In the hope that it wasn't a rat, my wife looked online to find out what kind of critter might make a hole five or six inches in diameter. The best matches were for a raccoon or a groundhog, which given that neither are endemic to the UK she deemed somewhat unlikely.
I do have a camera probe several metres long that I could poke down the hole to see what's at the end. However, if it is a rat — or, worse still, a stag beetle the size of a shoe — I don't want to disturb it.
I think I'll wait until we have a dewy morning then check out whether there are tracks leading from it and where they go.
Gawd, I hope it's not home to half a million bees.