Elderly council tenants and middle-aged "empty nesters" who want to move to smaller homes would get greater priority, under government proposals.
Ministers hope to free up larger homes
Ministers hope to free up more big houses for overcrowded families by helping those who want to "downsize".
Housing Minister Yvette Cooper said it would also be made easier to move to a different local authority area.
The government also plans to build 70,000 social homes per year at a cost of £8.4bn over three years.
In a speech to the Housing Corporation, Ms Cooper outlined plans to "refocus social housing around the needs of tenants" and to make it fairer and more effective.
She also announced extra funds to help 38 councils with the worst overcrowding problems and help for people to move across local authority boundaries.
It is thought there are about 500,000 overcrowded households - and about 445,000 "under occupiers".
The plans would see "reasonable preference" being given to people who want to move to a smaller property.
Other proposals include helping people move to social housing in other areas, or relocating to be nearer their family.
A government spokeswoman said it was up to councils to set their own criteria - but there was a national framework for social housing and if the consultation was favourable, the proposals would be included in them.
But she added: "We know it's really important to many people to stay in the homes where they brought up their families and which hold happy memories for them, and there's absolutely no question of this initiative applying to them.
"These proposals are designed to help people who no longer want to stay in houses which they feel are too big for them, or who want to move nearer to family or friends, for example to watch their grandchildren growing up."
In a written statement, the government announced that it would also be investing £2.4bn in the Arms Length Management Organisation (ALMO) programme.
This will result in a further 150,000 homes being brought up to standard, with four new areas - Charnwood, North East Derbyshire, Stevenage and Redbridge - also joining the ALMO scheme.