I really wouldnt recommend the Bridge unless the new managers, Fusion, make a serious attempt to clean this up as it has been filthy for a long time. The previous management famously never bothered making it hazardous for children. I found peanuts in there, filthy hankies stuffed under the matting and chewing gum stuck to the floors. They even had the cheek to charge a couple of quid for each child for the pleasure. Its not very well equipped nor large. Perhaps they'll turn it around however as its nice after a swim to sit in the cafe with a cuppa whilst the kids play.
Gambados is great although pricey and can be busy especially during the birthday party slots but is highly recommended on many fronts.
Rascals is fine too although becoming a little grubby and extremely busy. I can also recommend the Buzz Zone at Beckenham Spa as pretty good on all fronts especially for under 3's.
There is an excellent one for all ages at Peckham Pulse but its sessional so you need to check the times. There is a separate area for very young kids. Great to do on a wet Sunday afternoon.