I agree with much of what Roz writes - people round here do risk getting writer's cramp and with so many petitions of reducing impact, and that it's not fair to blame the Lewisham Council automatically.
Like Merlin, I too have enjoyed courses at the Kirkdale Centre, but when my course was cut, one enterprising member of the class found an alternative venue, made private arrangements, and the group still flourishes, without public money.
The building is a nice bit of architecture, but I can well believe it's not that practical to heat and maintain, so it's hard to ignore Dave Whiting's economic rationality.
There's a deeper problem for the Council, which is that it seems long since to have lost confidence in providing 'universal' public goods, such as adult education which is not justifiable by economic rationality - e.g. "E to E (education to employment) schemes for the 14 to 19s". Instead, its severely restricted spending has to be focused on the most needy. It's pretty hard to argue against this ... until you realise that the articulate, and relatively advantaged, such as readers and contributors to Forums such as this, no longer think of the Council as providing anything for them, other than maybe pothole repairs. With the loss universal services, a sense of social solidarity is lost.