Hi
I feel like I googled every venue too after getting engaged - sometimes there's just too much choice and it's so hard to come to that final decision! Anyway, here are some of the places I noted down in my venue search that might fit your bill:
If you don't mind having the ceremony and reception in different places then Orleans House Gallery out towards Twickenham is so, so lovely. There are lots of places round there for receptions too - The Wharf restaurant in Teddington is one that springs to mind but I know there are others too.
In central London there's a nice restaurant called Northbank which has a terrace by the river but you would have to have the ceremony somewhere else.
You could look at the Pump House Gallery in Battersea Park - it's by a little lake and, obviously, is surrounded by park. You can have both ceremony and reception there.
Lauderdale House in Highgate is another venue in a park - a friend of a friend had their wedding there and I've heard it's quite reasonable but obviously I don't know the exact details of the bill! They're also licensed for ceremonies.
Another waterside venue (although not with a garden, as far as I know) is the Canal Museum - you can bring any caterer you like to this one which can really help to keep the cost down. Unfortunately they're not licensed for ceremonies though.
The London Wetlands Centre near Barnes looked pretty cool and has amazing surroundings - I never found out the price though so don't know whether it suits your budget, sorry.
Some friends had their wedding at the Thames Rowing Club in Putney which is right on the river. The main room was really nice and I know they said it was a very competitive price. It's also licensed for ceremonies. You could also look at the London Rowing Club and the Auriol Rowing Club.
Anyway, I hope some of these help. I will let you know if I think of anywhere else.