Hello there,
We very nearly sent DS to the Greenwich Steiner school. We looked round it and loved it. Even DH liked it and he was very cynical! It was a tough call but in the end we sent him to a state primary.
I know people with kids there and they're very happy with the school.
My niece also went to a Steiner school (not the Greenwich one) - but transferred to a private school aged 7. My SIL got fed up with the: 'knitting and lentils' (her words!).
I believe that the Greenwich Steiner school is one of the more 'progressive' in that they - gasp! - allow computers in the Senior years.
Do you know much about the Steiner philosophy? If not, I would really recommend you do some research so you're fully aware of what you'd be signing up for. I won't say more than that.
You do know that the children don't do a full week of school (i.e 9am-3.30pm) until they're about 9? Personaly I think that's a good thing but obviously can be a problem for working parents.
Plus TV is frowned upon - but not actually 'banned'. And most parents haven't inoculated their kids.
I'm not sure where you are in Blackheath but there are some good state primaries you could have a look around? Although catchments are tiny. I also know kids at Blackheath private schools and there is a greater academic expectation of them in Early Years/KS1.
And I think there's a Montessori school next door to the Steiner school? Good luck!