In reply to Rafael: You don't say what climbing you have done before, but if you have done some, I'd suggest you walk from Swanage to Durleston Country Park, which is not far from the town. From there, find the lighthouse (it is obvious). Next to it (on the right as you look out to sea) is one of the most popular climbing areas at Swanage ("Subluminal") - you are likely to see people on the ledge area from which they abseil or climb down to the routes. If you go on a sunny day at a weekend, there are bound to be a lot of people there, and with luck you will find someone to climb with.
If your previous climbing has been on bolts, you might prefer to go to one of the bolted areas. I'd suggest "Dancing Ledge", which is around 5kms walk around the coast from Swanage and easy to find. There is a quarry there by the sea with bolted climbs - again there are always people there on a good day at the weekend.
There are a lot of other places people climb at Swanage, but those are likely to be best to meet people.
You might also want to try talking to this club:
http://www.southamptonrats.co.uk/
The area is beautiful and very "English" but also rather quiet - I hope you like it.