His series of five ‘tweets' drew an angry response from Allison Ogden-Newton, chief executive of local umbrella body Social Enterprise London.
Curley, whose organisation represents local infrastructure groups, asked whether social enterprise was "a respectable veneer for profiteers".
He also said: "Does calling your organisation a social enterprise give you a licence to do anything which makes money regardless of mission and values?"
And he questioned whether political enthusiasm for social enterprise was "an excuse to axe grants in the name of sustainability".
In an open letter to Navca, Ogden-Newton responded:"The social entrepreneurs I work with on a daily basis are some of the most brilliant, community-spirited, determined individuals I have ever met.
"To suggest that at the heart of social enterprise is anything other than the desire to achieve lasting social change is a gross inaccuracy.
"As the leader of an organisation that claims to be the national voice of local third sector infrastructure in England, I am surprised and disappointed at your apparent lack of understanding of the structures, aims and values of a crucial element of your sector."
The full response is available on the Social Enterprise London website. Curley was unavailable for further comment before publication of this story.