Brandon Lewis has promised £300,000 to Greenwich Council to help tenants buy their own homes on the open market.
The funding is among £18.48million that is going to be shared between 42 councils across the UK.
The Right to Buy Social Mobility Fund is intended to particularly help those looking to move for work, to be nearer to family, or those whose properties are difficult to mortgage.
Mr Lewis said: “The Right to Buy offers a helping hand to thousands of council tenants across the country to become homeowners – but some remain trapped in their own homes, unable to take up this opportunity.
“This fund changes that and offers people the chance to get on the property ladder and buy a home that best suits their needs.”
Tenants will be able to apply for support if they are able to support a mortgage but cannot buy the property they are in.
This could benefit older people who want to buy smaller properties or be nearer their family, or someone looking to move to take up a job opportunity. Alternatively, it could help those who are in properties that are difficult to mortgage because of the way they are built.
A decision has been deferred on whether to award a share of the fund to Tower Hamlets Council until it can provide assurances about its corporate governance.