Tony Blair has hit back at Theresa May after she accused him of “undermining” the UK in Brexit talks and “insulting” the office of prime minister.

As the highly unusual war of words between the sitting prime minister and one of her predecessors intensified, Mr Blair called Ms May “irresponsible” for trying to “steamroller” her Brexit deal through parliament.

Responding to her criticism of him, the former prime minister insisted it was “not irresponsible or insulting” for him to campaign for a fresh Brexit referendum and denied he had undermined her during negotiations with the EU.

Mr Blair has been a vocal advocate of the public being given a Final Say vote on Brexit and on Friday called on the EU to make preparations for the extension of Article 50 in order to allow more time for further negotiations or another referendum.

That prompted Ms May to launch a blistering attack on him.

In a statement, she claimed there were “too many people who want to subvert the process for their own political interests rather than acting in the national interest”.

“For Tony Blair to go to Brussels and seek to undermine our negotiations by advocating for a second referendum is an insult to the office he once held and the people he once served,” she said.

Mr Blair is understood not to have visited Brussels for several months, and it is unclear what prompted the timing of Ms May’s attack.

Supporters of a fresh referendum pointed out that she had not condemned former Conservative prime minister Sir John Major, who is also campaigning for another referendum and travelled to Ireland last week to call for the UK government to revoke Article 50 “with immediate effect”.

Responding to Ms May with a statement of his own, Mr Blair said it was clear that “neither the British people nor their parliament will unite behind the prime minister’s deal”.

He continued: “In these circumstances it is not irresponsible or insulting to put forward an alternative way to achieve resolution. The sensible thing is now to allow parliament to vote on each of the forms of Brexit canvassed including the prime minister’s deal.

“If they can’t reach agreement then the logical thing is to go back to the people. To describe such a course as an insult is a strange description of what would be the opportunity for them to instruct parliament as to how to proceed. Far from being anti-democratic it would be the opposite, as indeed many senior figures in her party from past and present have been saying.”

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In a clear attack on Ms May, he continued: “What is irresponsible however is to try to steamroller MPs into accepting a deal they genuinely think is a bad one with the threat that if they do not fall into line, the government will have the country crash out without a deal.”

He added: “I have always said, and did again in my speech on Friday in London, that I personally sympathise with the PM’s heavy burden in doing her job.

“I do not disrespect her at all. I understand her frustration. But I profoundly believe that the course she is pursuing will not work and is emphatically not in the national interest. And that’s the reason I am speaking out and shall continue to do so.”

Mr Blair is one of three of the four living former prime ministers to back a fresh referendum, with Gordon Brown and Sir John also supporting the calls. Only David Cameron has not done so.

Ms May is under mounting pressure to let the public decide the terms of Brexit in order to break the deadlock in parliament.