In reply to Charlie Revett:
Calshot is the only real option for an indoor wall.
See
http://www.calshot.com/climb.html
They are due to enlarge it (finally!) this winter, but it is OK - as an alternative Craggy Island in Guildford is worth the trip for a bit of variety. Other than that and the outdoor venues given in the previous post, you can get to the Wye Valley venues in about 2 hrs from the area.
Shameless club plug:
www.romseyclimbers.org.uk
Martin