Speaking at an event in London today, Timpson said that 95 authorities have now agreed to provide care leavers with a “setting up home allowance” of at least £2,000.
That figure is up from just 32 local authorities before a letter was sent by Timpson to directors of children’s services in October.
“I wrote to all directors of children’s services in October asking them to dramatically improve support for care leavers, and I have been encouraged by their positive response," he said.
"I now want all local authorities to commit to giving this support to care leavers.
“All care leavers must receive the right support and guidance they need to prepare them for their futures. No parent would want to see their children stepping out into the world without a roof over their head or a warm bed to sleep in."
A CYP Now investigation in 2011 highlighted the huge variation in the levels of support offered by councils to care leavers.
He added that regulations are being changed so that more 16- and 17-year-olds remain in care.
Decisions will now have to be "signed-off" by directors of children’s services if a young person is to leave care before the age of 18.
Natasha Finlayson, chief executive of The Who Cares? Trust, said that around one in three children currently leave care when they are 16 or 17, many of them encouraged to do so by their local authority.
"Most of them simply aren’t ready to live independently – they lack basic life skills like budgeting or cooking, and quite understandably struggle to cope emotionally when cut adrift from the support system and care they have been used to," she said.
"I hope that this new measure will lead to local authorities being better ‘corporate parents’ and doing all they can to encourage young people to stay in care until they are 18 and more ready to live independently.”
Timpson also revealed details of £280,000 in funding for two projects.
Under the £80,000 New Belongings project, being run by the Care Leavers’ Foundation, care leavers will be trained as consultants to work with five local authorities to improve local practice.
Meanwhile, £200,000 will be provided to the National Care Advisory Service (NCAS) to develop evidence-based models of delivery over the next two years to improve support and outcomes for young people leaving residential care.
“Today’s package of support, six months on from the introduction of the Care Leavers Charter, reinforces my commitment to make sure all young people have the chance to reach their full potential, no matter what their background," Timpson said.