There is a fantastic nursery school in Chertsey - that has a surestart centre attached (its a 'free' nursery so put name down asap)
over the summer holidays they run 'playdays' if you little girl is toddling about great safe space for her while you get to have a cuppa and a chance to meet lots of other local mums - email them saying you new to the area and they might fit you in.
you can google Chertsey nursery and get all the info for the surestart centre. There is loads to do around this area with little ones. Let me know if you get stuck on ideas , my kids are older at 7 and 4 but I will happily meet up in the park if you fancy a chat.