Council papers have revealed one o'clock clubs could make make way for more early-years care following new government legislation.
New policy will make it obligatory for local authorities to provide disadvantaged two-year-olds with 15 hours of free childcare.
Bolingbroke One O’Clock Centre, Triangle One O’Clock Centre , Garratt Park One O’Clock Centre and Earlsfield One O’Clock Centre are all listed as potential places for closure.
Balham Nursery School and Aspire Adult Education Facilities in Southfields were also listed.
Alex Sykes, 34, community manager of Made For Mums Wandsworth, said: "They have always served as community hubs to access other services. For a lot of mum's they are a lifeline, especially when you have got a small baby and you are feeling isolated."
Mrs Sykes, of Balham, has set up a petition against the plans which gained 120 signatures overnight.
A council spokesman said: "Creating such a large number of additional early-years education places is a major challenge and means the council is re-evaluating its current use of one o’clock club and children’s centre buildings.
"It is also consulting private and voluntary sector providers on innovative ways of working together, sharing sites and developing services."