In highly unusual move, Ms May hit out at one of her predecessors, claiming the former Labour leader’s support for a second Brexit referendum was “an insult to the office he once held and the people he once served”.
The criticism comes after Mr Blair told Europe to prepare for the “near probability” of Britain extending Article 50 to allow more time for negotiations or a fresh referendum.
The former prime minister has been one of the most vocal advocates of the public being given the Final Say on Brexit and has previously travelled to Brussels to make the case to EU leaders.
Ms May said: “I am fighting for a good deal for Britain. I will continue to fight for a good deal for Britain.
“I have never lost sight of my duty and that is to deliver on the referendum result and to do so in a way that protects British jobs, keeps us safe and protects our precious union.
“However there are too many people who want to subvert the process for their own political interests – rather than acting in the national interest.”
Condemning Mr Blair, she continued: “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.
“We cannot, as he would, abdicate responsibility for this decision.
“Parliament has a democratic duty to deliver what the British people voted for. I remain determined to see that happen. I will not let the British people down.”
It comes after Ms May called off a parliamentary vote on her deal with Brussels less than four months before Britain is due to leave the EU, after admitting the plan would have been heavily defeated.
On Friday, Mr Blair said a second Brexit referendum was now the most likely outcome.
“Our present situation is unique in modern British politics,” the former prime minister said in a speech in London. “The government is not in control – not of the agenda, not of the events and not of the outcome.
“What seemed a few months ago unlikely is now above the 50 percent likelihood,” he added. “We will go back to the people.”
Addressing EU leaders in Brussels, Mr Blair said they should offer to reform to make it more attractive for Britain to remain, including making changes to immigration rules, a key driver behind the vote to leave the bloc.
An offer by the EU to change would show “the political leadership of Europe and Britain had listened to the underlying concerns of those who voted Brexit, not disrespecting the concerns but meeting them in a way which is not damaging”.
Mr Blair said in most other situations, such as the time between engagement and marriage or accepting a job offer and taking it up, people can change their mind.
“If our knowledge of reality in any of these situations changed, in any of these situations would we really abhor the prospect of reconsideration?”
“Given all that has happened, the undemocratic thing is to deny people a final say.”
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