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We go to Little Fishes playgroup at St Peters Church, wickham road Brockley. 9.30-11.30 Mondays.
Tuesdays and Thursday mornings is a really nice playgroup at crofton park baptist church, huxbear street. Easily walkable from Ladywell.
Weds and thurs mornings is St Johns Church Playgroup on Loampit Vale.
So far I'm sounding like I love churches but they are cheap and you get tea and biscuits and kids get fruit.
Oh, nearly forgot Mondays and Fridays is a playgroup at Ackroyd road children's centre.
Brockley Central blogspot is a good website for one off local events and even more specifically LVIG have a blog, they are the ladywell village improvement group who have organised the Christmas market which is this Saturday.
I take my nearly 3 year old to Little Feet on a Tuesday morning at Rhubarb and Custard on Manor Lane in Lee which isn't too far from Ladywell. The toddlers seem to love it! sessions are drop in, or a cheaper rate to pay half termly.
Also, to be totally un-impartial, I run Caterpillar Music classes at Lochaber Hall in Lee on Thursday mornings and the ages range from 0-4yrs at the moment so you'd be welcome to come for a free trial!