Gordon Brown's pre-budget report this week may show a Chancellor losing his lustre but there is no doubt he still expects to be the next Prime Minister.
Amid speculation that Mr Blair will go if he fails to push through next year's education Bill, David Cameron, the new Tory leader knows that he is most likely to face Mr Brown at the next election.
But while Mr Blair's wish to increase parental choice, diversity and private-sector involvement in schools is well known, surprisingly little has been said about his neighbour's views on education.
As Chancellor, Mr Brown has presided over record increases in spending on schools. But an informal deal with Mr Blair has given the former free rein on schools policy, while Mr Brown's pronouncements have been largely limited to adult skills and the early years.
Nevertheless, there is a vague impression that a Brown premiership would be more in tune with traditional Labour thinking, and that he would be less willing to take on his own party and less zealous about reform.
In part this is a result of the role played by the Chancellor's allies last year in taking Mr Blair to the brink of defeat over tuition fees. He is also reportedly sceptical about foundation hospitals and increased private-sector involvement in public services.
But those hoping for a return to "real" Labour tend to gloss over the fact that Mr Brown, as much as Mr Blair, was the architect of the new Labour project.
On Radio 4's Today programme this week, Mr Brown said private-sector involvement in public services would be "intensified" in coming years and there would be no let-up in reform.
It was Mr Brown who tried to insist the Department for Education and Skills cap teachers' pay at 2 per cent for each of the next two years. And it is Mr Brown who has promoted the controversial private finance initiative to allow a massive rebuilding programme which gives private firms 30-year contracts to build and maintain school buildings.
Indeed, union leaders see him as more wedded to privatisation than Tony Blair, and less willing to compromise.
Perhaps most worryingly for those fed up with Labour's control freak tendency, it is the prudent Chancellor who insisted that the rises in school spending must be tied to improvement targets. The latest of these "public service agreements", in last year's spending review, contains 13 targets for schools including promises to improve literacy and numeracy, expand sport and cut truancy.
The review also demanded that the DfES produce efficiency gains of pound;4.3 billion by 2007-8, at least half of which, we are told, will be reinvested in front-line services.
While Mr Blair has become convinced that targets have largely played their part in school improvement, heads are concerned that his neighbour remains wedded to them.
From the early days of new Labour, it has been Mr Brown rather than Mr Blair who has done most to exasperate senior colleagues with his interference.
Described as "a megalomaniac" in private by a senior education figure, Mr Brown has at times left education ministers struggling to hide their confusion after changing carefully agreed policies when he announced them in a budget or spending review. He has also summoned early-years or adult education ministers to the Treasury to tell them how policies should develop. Pet projects such as financial education have been foisted on the DfES.
John Dunford, Secondary Heads Association general secretary, said: "This is not the way we want a Chancellor or a Prime Minister to work."
One area Mr Brown might be keen to extend targets is in raising achievement for deprived pupils.
While Tony Blair has often been accused of running education policies for the metropolitan middle classes, the Chancellor's willingness to tackle child poverty and adults who missed out at school suggests he will focus on helping those at the bottom of the heap.
In particular, the Chancellor is likely to have less sympathy than Mr Blair for schools that exploit loopholes in admission rules to avoid admitting what many Labour MPs see as their "fair share" of difficult pupils.
He is expected to slow down the creation of academies and be more willing to give councils a significant schools role - not least in the Every Child Matters agenda to boost child protection and support for disadvantaged children and integrate children's health, social and education services.
Ray Shostak, Mr Brown's adviser on education and public services, was previously director of children, schools and families in Hertfordshire, the first authority to combine education and children's social services. His views suggest the biggest change under Brown may be greater emphasis on collaboration rather than competition between schools.
In January 2003, Mr Shostak, then at Hertfordshire, told MPs that funding and accountability systems based on individual schools intensified competition between them. "At the end of the day, what parents want is high quality local schools," he said.
Could that mean league-table reform to remove the incentives for schools to cherry-pick pupils?
It is probably too early to say. But those hoping a change of PM will mean a change of direction can take comfort from the comments of a senior DfES civil servant. "Gordon Brown appears to believe in market forces everywhere except between the ages of five and 16," he said.