The Prime Minister and his leading allies are understood to have assured Mr Brown that he remains the only credible successor.

In an attempt to ease long-standing tensions between No 10 and the Treasury, Mr Blair has indicated that he expects to quit two years into the next Parliament if he wins a third general election.

This contradicts recent comments by Lord Falconer of Thoroton, the Lord Chancellor, who predicted that Mr Blair would remain in office for a full third term. The Prime Minister has resisted invitations to confirm these remarks.

Both No 10 and the Treasury are wary of any suggestion that there has been a deal. This is partly because of continuing controversy over the so-called “Granita pact” that Mr Blair and Mr Brown are alleged to have made in an Islington restaurant in 1994 over the Labour leadership.

The Prime Minister wants an end to the damaging rivalry that has existed between his aides and those of the Chancellor since then. Relations are said to have improved since discussions on the euro this year, during which Mr Blair acknowledged that he would quit and try to ensure a bloodless succession for Mr Brown.

The two men are also said to agree that a referendum on the single currency will be held early in the next Parliament only if the economic and political conditions are right.

On his return from holiday, Mr Blair will begin to restructure his Downing Street team in an attempt to shed the Government’s reputation for spin and political interference with the Civil Service.

Alastair Campbell, his director of communications and strategy, will not be directly replaced when he leaves this year. David Hill, a former Labour spin doctor who has been lined up for a senior role, is unlikely to get Mr Campbell’s powers over civil servants.

Jo Gibbons, another former Labour press officer and special adviser, is expected to take over Cherie Blair’s publicity, the job curently held by Fiona Millar, Mr Campbell’s partner.

The shake-up will attempt to bring about a clearer separation between political operations and the administrative work of civil servants. Tom Kelly, one of Mr Blair’s two official spokesmen, is still expected to be a given a more senior role despite this week’s controversy over his “Walter Mitty” remark about Dr David Kelly, the late government scientist.

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