Labour will not win the next election if it buries its head in the sand and denies that it will be decided in the centre ground, Lord Mandelson says on Monday in an interview ahead of the 20th anniversary of Tony Blair's election as Labour leader.

Blair is due to give a speech on 21 July to mark 20 years since he became Labour leader. It is likely to prove a challenge to those supporters of Ed Miliband who believe the country has moved to the left in the wake of the financial crash.

Mandelson, the Labour figure who, after Blair, is most closely associated with the New Labour project, says in an interview in Progress magazine that over the past two decades politics has moved further to the centre ground.

"Those who don't give their political loyalty automatically to left or right – whose votes, therefore, are up for grabs – are a greater segment of the electorate now than they were when New Labour was being created in the 1990s," he says. "Therefore, it is even more important now to win the centre ground to win electoral victory."

Although Blair's standing has fallen in the UK in the wake of the Iraq war and reports of his growing business interests, he is the only Labour leader to be elected prime minister at three consecutive elections.

Blair has himself acknowledged that new issues have emerged since he was last prime minister in 2007, but his willingness to make the speech shows he is determined to defend his political record from those who repeatedly distance themselves from the 1997-2007 governments, or claim Labour showed no interest in reducing inequality.

Although Mandelson's remarks are a commentary on the success of Blair, it is clear he wants Ed Miliband's team to draw lessons from his electoral success.

He says: "It is essential still to win on leadership and the economy, and to demonstrate that we are a party of conscience and reform that will talk to people's values and concerns, not simply keep driving an agenda of our own regardless of the electorate's views. That is why I get frustrated sometimes when people argue now that the country has moved to the left, therefore if we are more unambiguously leftwing and raise our ideological vigour, we are more likely to win the next election."

He says Labour needs to heed the lesson of defeat in 1992 under Neil Kinnock. He argues: "The truth was, however fed up people were with the Tories, they were not going to switch to Labour in sufficient numbers unless they were absolutely sure of what we were going to do in government … We had to demonstrate that we really could manage people's money and steer an economic course that would deliver sustainable economic growth and jobs."

Without naming Gordon Brown or his advisers, he claims they were out thought by New Labour and the Blairities, and were left in an "intellectual no man's land", trying to define themselves against Blair, but unable to produce an alternative agenda.

Blair's opponents in the party had to wait for the Iraq invasion before they could topple him, Mandelson says. "It gave them a stick to beat Blair with, knowing they were going to get media support, the rightwing media because he was Labour, and the leftwing media because he was New Labour. They hated his electoral success and Iraq was the opportunity to dislodge him."

Mandelson also rejects the frequent criticism of New Labour governments being uninterested inreducing inequality. He claims: "I would characterise New Labour's policies across the board as putting that desire to limit and reduce inequality absolutely at the heart of what made us tick."

He adds: "And I would defy anyone to identify a single policy area where we did not make progress in using those policies to reduce inequality. We may not have pulled off everything that we sought to do, at times our ambition might have been blunted, but it was never for want of trying during the whole of New Labour's time in government."

• This article was amended on 7 July 2014 to correct the year in which Blair resigned as prime minister from 2006 to 2007. The article was also amended to clarify that Blair was not the only Labour leader to win three elections, but the only one to win three consecutive elections.