My son with needs is older now but other parents have of children with needs are the best sources of info and support!
You can try:
Facebook groups (eg ASD SW London - appreciate your child may not be autistic but other parents in the group will have children with speech delay and sensory processing)
People who reach out to you from this post - feel free to pm me if you would like contact details for a few local WhatsApp groups that I know about etc - I am sure there are others too.
Contact - this is a charity that has a Wandsworth office and organises things like coffee meets or walks for parents of kids with needs. They’re a great source of info and support.
Wandsworth Early Years Centre based on Siward rd may be worth a call. I can’t remember what they offer now but in my sons early years they had playgroups, use of their soft play etc. also the Enhanced Early Years place somewhere on West Hill. (The Wandsworth council “Local Offer” site should have contact details).
SEN Talk another fab organisation that have coffee morning etc, aimed mostly at school age children and families.
Good luck. As I said please do feel free to PM me.