Their efforts are shown in papers belonging to the current shadow chancellor Ed Balls, which have been obtained by the Daily Telegraph.
The memos show they tried to get Mr Blair to stand down after Labour won a third general election in 2005.
Their plan was codenamed Project Volvo, the car Mr Brown's supporters believed voters most associated with him.
Mr Brown's supporters met on 21 July 2005, when Mr Blair was dealing with attempted terror attacks on London.
BBC deputy political editor James Landale says that - after gossip and memoirs dealing with the same topic - these memos document the extraordinary attempts to oust Mr Blair.
"Much of the detail may be for historians but the question is whether any of the revelations damage some of those on Labour's frontbench today who were close to Mr Brown, including the current leader Ed Miliband," our correspondent said.
A Labour source has said that this is all ancient history and that Labour is a party looking to the future, he adds.
'Muddled'
The Daily Telegraph has obtained more than 30 memos belonging to Mr Balls, one of Mr Brown's closest advisers.
The paper names current Labour leader Ed Miliband and shadow foreign secretary Douglas Alexander as co-conspirators.
The documents disclose details of secret meetings, opinion polls on Mr Blair's policies and attempts to rebrand Mr Brown's image.
They also include letters exchanged between Mr Blair and Mr Brown, which provide greater insight into the rivalry at the top of the Labour party.
The files show them haggling over the terms for a handover of No 10.
In February 2006, Mr Blair wrote to Mr Brown: "You (understandably) want me to go now.
"You need to be the candidate of continuity and change. The second will be relatively easy to do. A different person is, by its nature, change."
But, said Mr Blair, to be the candidate of continuity would require a "clear demonstration" to the public that Mr Blair, as the embodiment of New Labour, was "working hand in hand with the successor".
Suggesting a deal under which he would leave in summer 2007, Mr Blair said that in return he would need "full help and co-operation" on key reforms to the NHS, schools, welfare and energy.
And he warned: "Whilst I remain PM, the final decision has to be mine; and that cannot provoke a breakdown. I will try, at all costs, to avoid disagreement, but there can't be stalemate if it happens."
On a copy of the letter he passed to Mr Balls, Mr Brown scribbled the words "shallow", "inconsistent" and "muddled".