Temporary accommodation currently costs the authority more than £100 million a year.
Lambeth Council has put forward a series of changes to its Placement Policy, which has remained largely unchanged for a decade.
It expects the majority of homeless people will have to move out of the borough and even the southeast due to a lack of affordable properties.
Families with children in schools or specific care or medical needs will be prioritised.
Lambeth is now providing temporary accommodation for over 4,600 homeless households every night.
The council needs to find £183 million in savings over four years, with £99 million agreed and a further £84 million still to be identified by March.
Cllr Danny Adilypour, Deputy Leader of Lambeth Council and Cabinet Member for Housing, Investment and New Homes said: “Our new Placement Policy reflects the challenging reality we face – record numbers of families presenting themselves as homeless in Lambeth every day and unsustainable pressure on council finances caused by our increased need to source Temporary Accommodation to keep these families off the streets.
“We are determined to continue meeting our moral and legal duty to homeless families in Lambeth, whilst ensuring the financial stability of the council.
“Whilst this will mean placing families further away from Lambeth than they would like to be, we are determined to give them the stability and security they desperately need by giving them longer term placements in areas that will meet their family, cultural and community needs. This allow them to plan for the future, knowing they have a safe and secure home.”
