The Home Office is also preparing what it calls a "comprehensive action plan", for publication in the spring, to produce a "step change" in the level of service delivery by the sector.
The Downing Street meeting was described as positive by both sides, and Tony Blair has pledged to speak at a summer summit organised by the chief executives body, represented at Number 10 by, among others, Barbara Frost of WaterAid and Roger Howard of Crime Concern.
Nick Aldridge, director of strategy and communications at Acevo, said the meeting focused on the sector's potential in public service reform and delivery.
Discussions included the role of charities in running trust schools, as proposed in the education white paper that has met opposition from Labour backbenchers and former leader Lord Kinnock.
"We're suggesting an implementation team to move things forward," said Aldridge. "But the exact structure is up to the Government, obviously."
A spokesman for the Prime Minister said: "It was a positive meeting. He is looking forward to working with Acevo again in the future."
- See Editorial, page 22.