For a five year old who’s only just got a keyboard you do not need to have long hours of one to one piano lessons that could end up costing you lots of money and then discover that it was only the novelty bit that he liked after all. Far more important is that you help him to discover and develop a real love for music, out of which might flow a desire to play. He may get some of this at school, of course, but in the majority of primaries music is very low on the agenda, though there are a few exceptions.
Though it’s in SE5, if it’s easy to get to, you could try a visit to Camberwell Choir School on a Saturday morning (3’s to 6’s meet from 11am to noon in St Giles Hall Benhill Road). They work in little groups (which is far better at that age unless they have exceptional talent) and teach basic skills in keyboard, percussion, singing and drumming. There is no previous musical skill or knowledge needed and it runs on a donation basis, and they’re also very good at teaching basic life skills such as listening and working in teams and have groups for all ages from birth to 17. Have a look at www.camberwellchoirschool.org.uk
All of the suggestions sound great - I'd also recommend taking a look at The Music Boutique. Very reasonable rates and inspiring teachers in an engaging and creative environment. It's actually in SE11 but very easy to get to and on the route of the 344, the C10 also passes nearby. They offer half hour lessons after school or at weekends. My son 7 and daughter 10 have been going for a couple of years along with quite a number of other SE1ers. It's got a great reputation which is well deserved. No connection, just very happy with the classes .
I can also endorse The Music Boutique. My 6 year old daughter has been studying there for about 6 months and really enjoys it. Every term ends with a concert and she performed in her first one just before Christmas; we were both really proud!
For more information contact Osho on 07900 31 41 57.
I can also recommend the Music Boutique - my son  and daughter  have been going for 12 months and love it: they have a fun and engaging way with little ones too. Website is here which will give you a bit more info too: http://themusicboutique.org/piano.html
Again no connection, other than being a happy parent!