Indoors I would go for craggy island in Guildford, and if you can make the trip craggy island in Sutton, which is bouldering only. If you are ever in London then the arch at London bridge is also a bouldering only wall.
Outdoors there the closest is the southern sandstone bouldering at places like stone farm and Harrisons rocks, near tunbridge wells. However it needs a couple of dry days to be dry enough to climb, probably longer at the moment given the never-ending rain fronts.
Further away is the fantastic gritstone bouldering, at places like burbage south boulders up near Sheffield. Further away but really worth the trip - lots more rock, much nicer to climb, and they dry in about an hour after rain.
A quick google or ukc search of any of the wall or crag names should bring up details.
Hope the weather gets better for you,
Robert