Here are some out of borough activity centres that are highly recommended by Wandsworth families.
A charity based in Chessington which runs play activities for children/young people with special educational needs/disabilities and their families.
They have:
Family Play projects, supported by playworkers, for the whole family to attend and play together. For children ages 0-17
https://bookwhen.com/yordafamilysend
Forest activities for different ages groups in term time and holidays
https://bookwhen.com/forestadventures
Play and Care – Specialist child care for children aged 5+ with significant learning disabilities who need the support of a 1:1 playworker. There will be an assessment process to access this.
Contact: playleader.yordaadventures@gmail.com
Skylarks is a charity based in Richmond upon Thames. They provide activities and therapies for children with additional needs and disabilities and their siblings, plus information and support for their families face to face, and online. Most activities and talks are free.