Jeremy Corbyn has told an audience of European socialists that EU support for austerity has caused hardship for ordinary people, and that unless something changes there is a risk that “the fake populists of the far right will fill the vacuum”.

Speaking at the Congress of European Socialists in Lisbon, the Labour leader also said his party respected the result of the Brexit referendum and it was the duty of the left in the UK to “shape what comes next”.

Corbyn argued that Labour would be internationalist whether the UK was inside or outside the EU, and promised that the party would “work together to help build a real social Europe” by protecting workers’ and consumers’ rights.

He said: “EU support for austerity and failed neoliberal policies have caused serious hardship for working people across Europe.” It had “damaged the credibility of European social democratic parties and played a significant role in the vote for Brexit”.

However, he promised that under his leadership Labour would take a different approach, and he added a stark warning: “If the European political establishment carries on with business as usual, the fake populists of the far right will fill the vacuum. European socialists have to fight for a different kind of Europe.”

In a speech on the first day of the two-day event attended by Labour’s sister parties around Europe, Corbyn said of Brexit: “In a country where a million families are using food banks, over 4 million children are living in poverty, and real wages are lower today than they were in 2010, the British people voted to leave the EU. We respect that decision; it’s our job to shape what comes next.”

The Labour leader urged Theresa May to try to renegotiate her politically unpopular Brexit deal with the EU, using stronger language than before. “Further negotiations are a small price to pay to get a solution that works for us all,” he said.

Earlier this week Corbyn repeated his call for MPs to vote down the prime minister’s deal and consider an alternative, under which the UK would remain in the EU’s customs union and stay close to the single market. It is not clear how likely it is that this could be negotiated before the UK is due to leave the EU, at the end of March next year.

Corbyn criticised May’s refusal to take part in a TV debate with him before next Tuesday’s vote on the Brexit deal at Westminster, accusing the prime minister of trying to evade questioning in front of the nation.

“Unfortunately, when it came to it, as in the general election last year … the prime minister backed off and refused the head-to-head debate on offer,” he said.

Given the importance of the subject, he added, “this is the very last time for Theresa May to dodge scrutiny”.