In reply to Dave-Westlake:
Hi, There isnt anywhere in Reading itself. Most Reading people go to the Westway, Swindon or Craggy Island in Guildford, but the Westway is the best/biggest wall. Craggy is very popular though & does have a good bouldering wall.
You could so worse than to think about joining the Reading mountaineering club, they have a pretty good website.