Mile end leisure centre soft play - cheap and mostly always quiet if before the end of the school day. No need to book just turn up. Frog prince at Stepney farm on fridays. Thursday morning salvation army play & singing session £2. Weds morning St Annes Limehouse Chatterbox (loads of toys for different ages, snack time and songs). Feel free to message for more i have a doc could send over.
V&A Childhood Museum on Cambridge Heath Road… sessions start from 10am
Discover Children’s Story Centre in Stratford