Eddy Katz is crowded and stressful for a party, unless you book the whole venue, which is very expensive.
We organised one party at Kids Fusion and it was great; more expensive than the council-run recreation centres like the Wandle, near the Southside shopping centre (another good option) but not as expensive as Eddy Katz.
Another leisure centre with a softplay for parties is the Tooting one, near the hospital.
Also most churches have halls which can be rented for parties - but you must sort out the entertainment yourself (a bouncy castle, an entertainer, etc).
Kids would love Flipout but it's probably expensive.