Dallington School (independent primary) has a pre-school class that takes kids from 3 ( rather than waiting until the Step after they turn 3). Term time only and no wrap around so you would need to arrange these separately. Longish school holidays too - may or may not suit. Or try City Child in the Barbican - full nursery care 8-6, lovely outdoor space for the location. No personal experience but know people who were happy there albeit for slightly younger DC.