There is soft play at southbury leisure centre for £3.60 a session. I took my 8 month old and found him too young for it. It might be ok for your 15 month old but I think it is best for slightly older kids.
There is one in Whetstone next to the Audi showroom, it used to be called Kids at N20, but I think they have changed their name since.
I've been there with my lo, who also had a birthday party there. Have not been for a year, as lo is into other things now, but when we used to go it was very clean, their cafe got 5 stars from the council for food hygiene and there are different sections for age groups.
There is one in palmers green, but I've heard it is dirty, so have not been there. The only other place is clown Town in friern barnet at the back of the big tesco.
Nearer to you is KidzBiz in Palmers Green, which is hidden behind McDonalds. You enter via the car park on Lodge Drive. However, for a 15-month old, Southbury Leisure Centre would be a better option. Southbury has a dedicated area for under 2's and another area next to it with a small slide and ball pond for 1-5 year olds. There's also an area for bigger children up to 8 years old, (although my 2 year old plays happily in the bigger kids area). Southbury also has the advantage of free parking if you're driving. You have to pay the standard car parking charges at Palmers Green, which adds to the cost of your trip.