Thought i would post this as i needed it when i moved here a few months ago.
www.kingston.gov.uk/browse/community_people_and_living/children_and_young_people/children_s_centres.htm
My local centres in New Malden and Norbiton are great for meeting mums with under ones.
I also found a good cafe where the little ones can play called
Jellybugs Play Cafe
The Rotunda, Clarence Street, Kingston Upon Thames Surrey kt1 1qj