This sounds like 1pm by the padling pool for a picnic, unless it is horrid weather...the cafe in Brockwell isn't as nice as Dulwich, but we'd just cope I suppose!
The paddling pool is sort of directly over the other side of the hill from Whippersnappers. If you don't want to struggle over the hill with babies, bags etc, the road that leads into the park from the other side, nearest ther playground, is probably nearest. I'll check what it's called.
New thought: the cafe at the Lido may well be open...I'll do some research and post over next few days or Monday.
Would that timing be ok for you Twiglett...sounds like a bit of a dash.
And SAHMumster - can you make it then?