Theresa May is to face fresh questions over her Brexit plans after the European parliament was informed it was the British prime minister who first raised the possibility of extending the transition period beyond 2020 with the EU’s leaders.

Donald Tusk, the president of the European council, told MEPs it was May who brought up the idea at last week’s summit, despite the prime minister’s public claims that she is vehemently opposed to such a move.

Tusk said: “Since Prime Minister May mentioned the idea of extending the transition period, let me repeat that if the UK decided that such an extension would be helpful to reach a deal, I am sure that the leaders would be ready to consider it positively.”

Under the terms of the 21-month transition period so far negotiated, the UK would continue to live under EU rules and laws, but without any say in their design, as the country would not have any representation in the bloc’s institutions.

The prime minister was already on the back foot on the issue after cabinet papers leaked to the Times revealed that the UK could be locked in a transition period lasting years rather than the few months she has promised.

The documents reportedly say the plan to maintain an option to extend the transition period, known as the implementation period or IP in Whitehall, “could, in theory, lead to a long-running IP”. They say the arrangement could last for many years on a rolling basis with an annual decision point for its renewal.

The former Ukip leader Nigel Farage, who remains an MEP, immediately seized on Tusk’s comments. “Mr Tusk, I want to thank you for confirming that it was Theresa May that asked for the one-year extension to the transition period,” he said.

Nigel Farage arrives for the debate in the European parliament. Photograph: Frederick Florin/AFP/Getty Images

The debate in the European parliament in Strasbourg was also notable for an impassioned speech by the European commission vice-president, Frans Timmermans, who signalled his belief that the British public had the right to think again about Brexit and asked whether the Tories, “the party of Churchill”, had been “eaten by Ukip”.

His comments came in response to an attack by Syed Kamall, the leader of the group in which Tory MEPs sit in parliament, on the socialist group’s leader, Udo Bullmann.

Bullmann, a German MEP, had moments before broken from Jeremy Corbyn’s position and backed a new Brexit poll, leading Kamall to claim that the Nazis had been socialists.

Timmermans accused Kamall of aping the language of Farage. “Is it as Churchill predicted when he talked about appeasers. The only thing you get by feeding the crocodile is that the crocodile will eat you last?” the former Dutch foreign minister asked.

“Has the Conservative party finally been eaten by Ukip? I hope not. I do hope not. I say this because I will make no secret of my deep admiration and affection for the UK and everything it has achieved during its history … The European Union is an instrument to help European people solve their differences at the negotiating table instead of the battlefield.

“The European Union is a guarantee that no British soldiers will have to be sent to battlefields in Europe again as they have so valiantly done in our common history. The European Union is the best guarantee for peace in Europe for the ages to come and for one of the biggest member states to leave is an incredibly sad moment and I want to say that in this house. As a democrat, indeed as a human being, who in this house has never ever changed their minds on anything? But we will leave that with the British people. That is not for us to judge.”

Frans Timmermans delivers his speech. Photograph: Frederick Florin/AFP/Getty Images

The EU leaders’ summit last week had been intended to be a “moment of truth” in the Brexit talks that would reveal the path towards a deal. Tusk informed MEPs, however, that the British government needed more time before it could strike a deal with the EU, but that he was ready to call an extraordinary Brexit summit of leaders should there be a breakthrough in the talks.

Tusk said: “Last Wednesday evening, leaders listened to Prime Minister May’s views on the negotiations.

“Afterwards, the EU27 met in the article 50 format, with our chief negotiator, Michel Barnier, to discuss the state of play. It was made clear by the UK that more time is needed to find a precise solution. Therefore, there is no other way but to continue the talks. Leaders expressed their full trust and support for Michel Barnier.

“President Juncker also touched upon preparations for a no-deal scenario, an outcome which we hope never to see. And, of course, I stand ready to convene a European council, if and when the union negotiator reports that decisive progress has been made. The Brexit talks continue with the aim of reaching a deal.”

He also blamed Brexiters for the resurrection of tensions over the border between the Republic of Ireland and Northern Ireland.

“We want to avoid a hard border in Ireland. but there is no guarantee that we can do it. And you know why, Mr Farage? Because Brexit is defacto a political decision to establish the border between the union and the UK. Brexit is a project to separate the UK from the EU,” he said.”

“I don’t know what is going to be the result of the negotiations but I do know that it is the Brexiters who are 100% responsible for bringing back the problem of the Irish border.”

The European parliament’s Brexit coordinator, Guy Verhofstadt, told the same meeting of MEPs that until the issue of the Irish border was agreed, nothing was agreed.

“We are now in a battle of the figures. Mrs May says 95% has been agreed, Michel Barnier says 90% has been agreed. I know Britain has always had difficulties with the metric system. If it is 90% or 95% or 99%, if there is no solution for the Irish border, for our parliament it is 0% that is agreed at the moment,” he said.