Tony Blair has predicted that Gordon Brown will not try to reverse his legacy of public service reform if he becomes prime minister.
Tony Blair says Gordon Brown backs his reforms
Mr Blair told BBC News his ambition before leaving Downing Street was to ensure changes to healthcare and education "bedded down".
But he insisted Mr Brown and other Cabinet ministers backed efforts to increase choice in public services.
Mr Blair has said he will stand down before the next election.
He has pledged to serve a full third term in office.
Interviewed in New York for Radio 4's Today programme, Mr Blair was asked about his ambitions in domestic politics before his retirement from No 10.
He said: "The key areas are the seeing through of the reform process in the health service and in our schools, so that you keep absolutely true to the principle of equality in terms of access to the health service, in terms of equality of opportunity in our education system, but you make that a reality for today's world."
He wanted to ensure people could access high-quality healthcare and schooling whatever their wealth, he said.
Asked about whether he wanted to make changes which were irreversible by his successor, Mr Blair said: "If what you really mean is do I think that Gordon or anyone else is going to turn around and reverse those changes, no, he is fully behind the change programme, both in health and education.
"I think it is important to realise these are not policies simply that I have devised, these are policies taken through by the whole government. And the reason we take them through is that they are working."
Mr Brown is thought to be less enthusiastic than the prime ministers about some aspects of the government's reform agenda such as Foundation Hospitals, which give more financial freedom to hospitals.
Mr Blair was among a number of senior politicians who joined former US President Bill Clinton for the launch of a new anti-poverty programme on Thursday.
Asked if he would be hosting similar events after leaving power, Mr Blair replied: "I haven't the faintest idea. And it is not what I'm concentrating on at the moment.
"You have got to get on with the job in hand and let the future look after itself."