In reply to Cerith:
The simple answer: three words... is: The Orange House. There are normally lots of good people there with whom to climb. There also seems to be quite a regular bunch normally based in Calpe.
A couple of months ago, a lady was staying in Altea and made a similar enquiry. There was a long, detailed thread. If you do a search, you'll find it. But these are probably the best options.
Just noticed you're in Torrevieja - sorry, can't remember how far that is from either venue.
Mick