Launching the Housing and Regeneration Bill last week, junior housing minister Iain Wright said the agency will challenge councils that fail to supply enough homes towards the target for three million by 2020.
It will have the power to issue compulsory purchase orders and act as a planning authority in some areas, subject to approval by the secretary of state.
The bill says the agency will be able to allocate funds for infrastructure such as transport, shops and community facilities to encourage councils to build homes including social housing.
Wright explained: "We need to build between 45,000 and 50,000 social homes in the next few years. We need local authorities to be at the very heart of house building because they know what their local needs are."
The agency will bring together English Partnerships and the Housing Corporation. It will also take on responsibility for the Academy for Sustainable Communities.
The British Property Federation welcomed the bill. A spokesman said: "Moves to supply affordable housing are welcome. By looking to empower local authorities the government will enable communities' needs to be fully taken on board."
He added: "Prioritising housing and infrastructure provision is essential. But we hope that ministers can look for fresh solutions to housing people."