The Department for Work and Pensions' Right to Bid scheme should be extended to every part of national and local government, according to Peter Kyle, deputy chief executive of Acevo.
He raised the idea at the Conservative Party's Social Action conference last week in response to a request from shadow home secretary Chris Grayling for suggestions on how to make government more efficient.
Under the Right to Bid scheme, charities that think they could run DWP services more efficiently can submit proposals to run them.
Kyle said extending the scheme across government would bring "tremendous pressure from the ground up to improve services".
Grayling, who was shadow work and pensions minister until January, agreed to consider the idea, according to Kyle.
The conference was also addressed by Conservative leader David Cameron, who has encouraged Tory election candidates to volunteer for local organisations.
Kyle applauded the initiative but said candidates' positive experiences needed to be converted into detailed thinking about how that would affect Tory policy in a future government.