Thruxton is about as South as you can get, near Andover. Brands Hatch is near Dartford, so not that far away as well. Silverstone is not all that far away either.
Rockingham is quite far away (near Leicester). If we're going that far we may as well do a decent track like Cadwell with some hills in it. Rockingham looks flat and boring to me.
I guess price will be the factor here, I will also have to purchase a leather jacket and maybe even new trousers before doing a track day so I might be out of contention.
There is also Castle Coombe near Bath, great little track.
