The former Labour prime minister also said that Brexit is a “distraction” from the real problems facing the UK as he called for parliament to provide solutions to “actual problems” facing communities.
Blair’s comments come after he put his name to a report calling for tighter domestic controls and the negotiation of modified free movement rules with the EU.
This would fulfil the will of the people expressed in last year’s Brexit vote while allowing Britain to stay in the EU, and Jeremy Corbyn’s Labour should back the approach, he said.
Blair told BBC’s The Andrew Marr Show on Sunday: “This decision is life-changing for this country and this is a moment when every member of parliament... has got to see if there is a way of meeting people’s legitimate grievances and anxieties that gave rise to that Brexit vote, but do it in a way that doesn’t undermine the economy of the society and the country and its standing in the world.”
Blair has been blamed in many quarters for the rise in public concern about immigration which culminated in the Brexit vote, after failing to impose transitional controls on migrants from new EU member states in 2004.
But he said the situation was different 13 years ago and when he left office in 2007 - before the recession.
He added that non-EU immigration was of “bigger concern” for most people.
Addressing concerns about jobs and immigration, Blair said: “If we want to deal with those questions we can deal with them without the sledgehammer that... through Brexit, destroys the EU migration that we actually need... and it doesn’t of course deal with the other parts of the immigration issue, which I think are a greater concern.”
Blair’s intervention appears designed to provoke a fundamental shift in the Brexit debate and solve the seemingly intractable trade-off between the economy and immigration.
Blair told Marr: “Brexit is a distraction from the real problems this country faces.
“If parliament really believe that then their obligation is to set out solutions that deal with the actual problems that communities and problems have and not do Brexit that is actually going to distract us from those solutions and going to cause real economic and political damage.”
Prime Minister Theresa May has made controlling immigration her absolute Brexit priority but Brussels has stressed the UK will have to leave the single market if it wants to end the free movement of EU nationals.
But in an article for the Sunday Times website, Blair said: “There is no diversion possible from Brexit without addressing the grievances which gave rise to it. Paradoxically, we have to respect the referendum vote to change it.”
He went on: “We can curtail the things that people feel are damaging about European immigration, both by domestic policy change and by agreeing change within Europe. This is precisely the territory the Labour Party should camp upon.”
But he said “back then the economy was strong, the workers needed”, adding: “The times were different; the sentiment was different; and intelligent politics takes account of such change.”
Brexit voters’ concerns about “pressure on services”, “downward pressure on wages” and “cultural integration” now “cannot be ignored”, he said.
According to the newspaper, a report from the Tony Blair Institute, authored by former Downing Street policy expert Harvey Redgrave, urged the Government to:
Force EU immigrants to register on arriving in the UK so authorities can check whether they go on to work or study, a measure already in place in Belgium.
Make EU nationals show evidence of a job offer that is confirmed by their employer before they enter Britain.
Ban those without permission from renting a home, opening a bank account, or accessing benefits.
Introduce “discriminatory” controls restricting EU immigrants’ access to free NHS care if they are “economically inactive”.
Let universities charge EU nationals higher tuition fees than British students.
Try and negotiate a change in free movement rules to introduce an “emergency brake” on people coming into Britain when public services are overstretched, which David Cameron attempted but failed to secure when renegotiating the UK’s EU membership ahead of the referendum.
Blair added: “If we go ahead with Brexit, we will have taken the unprecedented decision for a major country to relegate ourselves, like a top-six Premiership side deciding to play exclusively in the Championship.”
Tory grandee Lord Heseltine also suggested the EU could be open to reform of free movement after the German election this month, while criticising “damaging” proposals revealed in a leaked Home Office document this week.
The peer said immigration as an issue was a “low hanging fruit” for politicians, who blame it for pressure on public services despite its contribution to the economy in an effort to win over voters.
Addressing the Home Office plans in the Mail on Sunday, he wrote: “Free movement of labour would end immediately and all but the most highly skilled EU workers deterred from coming to this country.
“I fear the very social fabric of our caring society, health services and swathes of the public sector which depend on immigrant support could be destroyed if this happens.”