Earlier in the day, May had confronted the European commission president, Jean-Claude Juncker, accusing him of calling her "nebulous" in a press conference. "This agreement, I believe, is truly good for both parties and it is the only one possible", he said.
Paul Williams, MP for Stockton South, echoed support for a second referendum, as he argued that if Mrs May can change her mind about her Brexit deal, then she should accept the public has changed their minds too about the EU.
The French president, Emmanuel Macron, said the Brexit deal was now "in the hands of the British parliament" and called on MPs to take a clear position on whether to accept or reject it.
The UK press seemed to enjoy the actions of the oft-maligned PM, with tabloid newspaper The Sun saying she was giving Mr Juncker "an earful", while the Daily Mail compared her actions to those of former British prime minister Margaret Thatcher when she "handbagged" European Union leaders in 1984.
The Prime Minister addressed the EU27 leaders on Thursday about MPs' concerns about the backstop which had prevented her getting her Brexit deal through Parliament this week.
With more than 100 Tory MPs and her DUP partners now opposed to it, the deal faced certain defeat on a scale likely to kill it off forever.
"I was following the debate in the House and I can not see where the British Parliament is heading at.' To laughter from journalists, Mr Juncker said: 'In the course of the morning, after having checked what I said yesterday night, she was kissing me".
She said that, as formal conclusions from the summit, they had "legal status" but added: "There is work to be done".
"I was not addressing her, and in the course of the morning after having checked what I said yesterday night she was kissing me", added Juncker, who is known for his affectionate and tactile approach to European leaders.
Mrs May had appeared to come away virtually empty-handed from the summit.
Mrs May insisted she had been "crystal clear" about the UK's need for firmer assurances that the backstop can not become permanent.
Juncker later explained that he was talking about the overall debate in Britain, where it is often hard to tell who is on which side, not referring to May personally.
Speaking at a summit in Brussels, she said there was still "work to do" but there had been progress and talks over "further clarification" would continue.
The Irish backstop is created to prevent the emergence of a hard border on the island of Ireland if trade talks falter.
A draft text negotiated on Wednesday noted: "The backstop does not represent a desirable outcome for the Union".
And gesturing to Austrian Chancellor Sebastian Kurz, he joked: "It will happen to Sebastian in a short period of time".