Madmaz, thanks in advance for getting info on The Tramshed.
As for 'The Woodcraft Folk'. Here I sigh, because I have a friend who is really heavily into it as child and adult and could post paragraphs of passionate and informative stuff here. Her mother is still a leading light in the movement in her local area. I am not her, so you will have to make do with my vague answer.
The Woodcraft Folk was part of the co-operative movement. It was a left-wing and athiest/humanist answer to the right wing and patriotic/christian roots of Baden Powell's boy Scout movoment, started during? after? the First World War.
The Woodcraft Folk is still going strong. There is a group in Lewisham. Not one in Greenwich, Blackheath, Eltham or Woolwich, to my knowledge. Although formed for children, both teenagers and adults seem to be very active in the groups as well. Music, story telling, saving the planet, world peace, cooking together and camping feature heavily. The summer camps see other groups from abroad visiting. I get the impression it is all a little on the gentle, folk-singing hippy side (and there's nothing wrong with that!), but definitely not designed for the out-and-out bender-living crusty.
I would have got my son involved, but the nearest group is too far away. If he wants to go to it at a later date when he can make his own way there, possibly, he may swap over from the more traditional, church-orientated scout group that he currently attends. Up to him, really.
Babynick (ex-Blackheath) Hi! No, my son does not go to the scout groups you mention. Is 'Musical Theatre' a children's theatre company? Just wondered.