In a speech in Liverpool, the prime minister said groups should be able to run post offices, libraries, transport services and shape housing projects.
Also announcing plans to use dormant bank accounts to fund projects, Mr Cameron said the concept would be a "big advance for people power".
So should the plans be implemented in Thornbury and the local area what would you like to run? What do you think you could run better?
The prime minister said that community projects would be established in four parts of the UK - Liverpool; Eden Valley, Cumbria; Windsor and Maidenhead; and the London borough of Sutton - as part of efforts to "turn government completely on its head".
But we would like to know what in Thornbury you would like to change, if you were given the chance to take control of a local project or service what would it be and what changes would you make.