The former prime minister said concerns about immigration from non-EU countries was “upending politics” all over Europe and the only way Britain could try to turn the tide on Brexit was to take these worries seriously.
In a major speech on globalisation in London, Mr Blair was expected to say that Theresa May could be forced to delay the official exit day in March due to the political impasse over Brexit.
Ahead of the speech, he told the Today programme: “This is a huge problem for Europe and it’s undoubtedly driving the populist forces across Europe.
“I think what you will see this weekend [at the European Council] is a recognition by European leaders that they do have to deal with this otherwise this populist movement is going to grow and grow in intensity.”
The West is losing sight of the values that brought the US and Europe together and Donald Trump must be persuaded to preserve international alliances, Mr Blair will tell the Chatham House think tank on Wednesday.
He said: “If you want to defend globalisation, which I do because on the whole it has brought enormous benefits, then you have got to deal with the underlying anxieties people have about it, of which immigration is the principal one.
“That’s exactly the same by the way with the Brexit debate. You are not going to release ourselves from Brexit unless we make sure that we are tackling the immigration problems people are angry about.”
In his speech, Mr Blair will acknowledge that supporters of globalisation are on the back foot as left and right-wing populists argue against free trade, migration and international alliances which are "portrayed as contrary to putting national interest first".
"Once it is clear the populism isn't working because, ultimately, it offers only expressions of anger and not effective answers, the populists may double down, alleging that failure is the result of half-heartedness and that only more of the same will work," he will warn.
"Who knows where the dynamic of that scenario takes us. Then the comparisons with the 1930s no longer seem far-fetched."
Calling for "new thinking and muscularity in defence of reason", Mr Blair will warn: "We are losing sight of the values which brought the West together, saw it through the menace of fascism and communism and, for all our justifiable grievances, have wrought immense progress."
The ex Labour leader will also use the address to hit out at both the Tories and Jeremy Corbyn's party over the state of the Brexit process, demanding a more assertive parliament and a fresh referendum on any deal with the EU.
"We should plan now for the possibility we need to extend the March 2019 deadline," he will say.
"Presently, we are drifting towards March 2019 with no clear negotiating position, no resolution of the Northern Ireland question, still vaguely hoping Europe will allow us access to the single market without abiding by its rules which it will never do, and with senior cabinet members openly debating the merits of a negotiating position which 'threatens' Europe with a no-deal Brexit.
"This is the equivalent of holding a negotiation on the top floor of a high-rise building and 'threatening' to jump out of the window if our demands are not met. The whole thing has become so protracted that it has numbed our outrage."
Mr Blair said the prime minister was "more a hostage than a leader" while Mr Corbyn "neglects to lead the fight here at home over an issue which literally determines the future of Britain".
He repeated his calls for a second referendum on the deal, adding: "Parliament must assert itself because neither government nor opposition can or will."
It comes as shadow Brexit secretary Keir Starmer made a similar intervention as he embarked on a two-day trip to Brussels, saying the deadlock in the Brexit negotiations was stoking European fascism.
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