Tony Blair is to take his most active part in the Labour party since retiring from frontline politics, contributing ideas and experience to Ed Miliband's policy review.

Blair, who stepped down as prime minister five years ago, will be giving advice on the Olympic legacy and in particular how to "maximise both its economic and its sporting legacies", Miliband said last night.

The role reflects Blair's part in the successful 2005 bid to host the Games and his sporting foundation, one of the key charitable causes in his retirement.

Blair will be reunited with leftwinger Jon Cruddas, a former aide, who was brought in by Miliband to head the policy review. Cruddas spoke recently of "reforming the band" – bringing together leading lights of New Labour – in support of Miliband.

The controversial move – perhaps especially within the Labour party – was announced at a fundraising event when Miliband and Blair symbolically shared a platform to make speeches.

Miliband, who was more closely allied to Gordon Brown during the 13 years of Labour government, declared that Blair's help for the party marked a "coming together of the Labour tribe".

The Labour leader said the party could learn three lessons from its most electorally successful prime minister. These were the importance of unity; the importance of evolving new ideas for new times; and the importance of winning to ensure that Labour does not allow the people whom its MPs are elected to serve are not abandoned.

Miliband also praised Blair's role in helping the UK win the right to host the Olympics this summer. It was, said Miliband, "one of the many proud achievements of the governments that Tony led: saving the NHS, rebuilding our schools and cutting crime".

"I want to thank Tony for what he did for our party and for our country. And I know how committed he is to Labour winning next time."

Blair told the Labour fundraising dinner at Arsenal's Emirates stadium: "It's an honour to be here tonight to support our party, whose values and principles I have always believed in and always will.

And to support Ed, support his leadership, support his drive to make our party win."

The joint appearance was organised by Alastair Campbell, Blair's spin doctor for his first six years as PM, the former Labour general secretary Lady McDonagh, and Richard Caborn, sports minister during the successful Olympic bid. Other guests at the event included the former deputy prime minister Lord Prescott.

The Manchester United manager, Sir Alex Ferguson, who had hoped to attend, sent a letter of support. Campbell read out the letter in which Ferguson said he hoped David Cameron would be a one-term prime minister, just as he hopes Manchester City will be one-season champions.

With much of his own party – and the country – still angry about the legacy of Blair's decision to take Britain into the Iraq war, and Labour's clear departure from socialism under his reign, Miliband will be aware that Blair's new role will not be universally welcomed.

Last night aides played down Blair's policy position, saying it should not be "over-interpreted".

"It's something Tony knows a lot about," said one insider. "He's got the sports foundation and he was instrumental in bringing the Games to London."

In an interview last month with the London Evening Standard, to mark five years since he stepped down as PM and Labour leader, Blair was asked if he would return if he were asked to be prime minister again: "Yes, sure, but it's not likely to happen, is it?"

Otherwise, he was coy about what sort of role he could play in public life, adding: "What I can do is contribute to the debate, whether it is Europe or the Arab spring or areas to do with economy and public service reform here."

He was less shy, however, about giving contentious views on the current economic and political turmoil, his views potentially at odds with Miliband's talk of rethinking capitalism and a revolution in banking.

"I think the hardest thing for any political party now is to work out what has really changed since the financial crisis and what hasn't," Blair said.

"My view is that you still, in order to win from the Labour perspective, have to have a strong alliance with business as well as the unions.

"You have got to be very much in the centre ground on things like public sector reform. But I understand that some people think the financial crisis has altered everything. And the mood is against this.

Personally I don't think that's correct."

Cruddas, who became Blair's link with the trade unions between 1997 and 2001, believes the New Labour pioneer started well as an ethical socialist but then came to a "dismal end". Significantly, friends say he argues that Blairism should not be remembered as it was at the end of the former PM's tenure, but the early days: "Labour has to get back to what Blair deserted," said one ally.

As well as his political legacy, Blair remains controversial in retirement for his globetrotting activities and the vast sums of money he has made, including relationships with Portland Communications, which has advised the government of Russia, and the investment bank JP Morgan Chase.