In reply to Rachelouise:
Hi
You could try The Rock Court at the Stanley Deason Leisure Centre in Brighton, and possibly a bit more local to you than Adur in Shoreham.
Rock Court info here:
http://www.aultd.org/climbing-wall/
I've climbing regularly at both walls, as benota says, check the partners wanted notices.
Recently I've been taking my 4 year-old daughter along to the kids climbing session at the Rock Court, which she's absolutely loving, and the instructors are very patient with all the kids.
Cheers