Yes, the nearest to each other, not for the whole country. There are plenty of teams who are actually closer to each other.
I was watching a video not long ago when someone visited the grounds closest to each other. That Dundee/Dundee United one is insane with how close they are. I brought it up on Google maps street view afterwards and had a look.
My local boys used to have a huge rivalry with Colchester, which when you look at the map it's a ludicrous one, as they're 100miles apart. But it goes back to some huge non league battles.
These days we're about 24miles off Reading, 30miles from Oxford and 40-50miles from MK within the same county.
But none of the fans like to admit any of them are "derbies" at all.
Our "traditional" derby was probably against Slough Town, a mere 12miles away, but obviously long lost in the sands of time as despite them having a resurgence to the Conference south, we'll never play them again realistically.