I've visited many of the schools mentioned here for my DS and found that:
Putney Park - were very approachable... a little too approachable and too keen gave away a small teddy for the visit!? I also had the impression that their strengths were more towards building self confidence and esteem as opposed to academics.
Merlin - Felt like a strong school that aspires to achieve more than it currently does (which is a plus), and were far from snooty.
Hurlingham - Funny uniform, but I met someone who wants to send all 3 of her children there (one there already) so they must be doing something right! Receptionists were very helpful.
Prospect House - I definitely found them to be the best non-assessed entry private school in the immediate area. They provided extra sessions for the weaker pupils. The facilities appeared modern, and IT was quite uptodate (although I can imagine it could benefit from do a little refresh over the coming year or two), places are limited (and waiting lists are long, which says it all). Having said that, I heard they are expanding the school and therefore doubling the number of places available, this is both a positive and negative as it could affect teaching standards. They are my first choice school for my DS if he gets offered a place (I woud happily lose a terms deposit, ouch, if we got a late offer from them... but that is primarily because it would save an hour and a half of school runs a day as my DD is at Putney High School).
Putney High School - My DD went for 6 junior school assessments and got 3 offers, she went to most of the school visits too and she said she liked it the most (assessments too) and wanted to go there and so it was a no brainer when they made an offer. Their assessments were by far the most efficiently run and parent friendly. Like most GDSTs they are academically strong but want children to be confident and open. I guess they have to be pretty confident to wear bright purple. They assigned a buddy from a older year to each reception child to help ensure they feel safe and wanted from day one, my DD loves her one. I was also amazed how many older girls said good morning to her by name during the 2nd week of her starting.
Roche - I only visited the nursery, but was put off when they said that they expected to require children to do 5 days a week upon starting (at 2 years old!?) However I have to admit I loved how well they managed they were and how calm the classroom was.
Lion House - Based in a church, the early years get to use the upper LARGE floor/room. They seemed rather nurturing and friendly. Shame about the outfit the young ones have to wear. I will be sending my DS here, he just loved the place and didn't want to leave (nothing more important than making sure your DC have a love of and wanting to go to their school).
Noddy's nursery - Fantastic facilities! I wish I went there as a child (assuming my parents could afford it). They operated hours that were longer than normal working hours allowing the parents to do drop off and pickups (and without the need of making breakfast and lunch). Just a shame the cost was much steeper than all the other places and that my DS was scared of playing with a class as we visited the rest of the nursery.