Theresa May's calm anger is a bid to balance humiliation

Tom Rayner, political correspondent

If there was any doubt how shaken the prime minister was by the very public snub of her Chequers plan meted out by EU leaders in Salzburg, there is none any more.

In her press conference on Thursday she looked rattled, perspiring as she tried to answer questions on a situation that had gone off script - the summit that was supposed to generate some positivity for her approach, ending in what some newspapers described as "humiliation".

Indeed her Brexit secretary confirmed on Friday he thought the prime minister had been ambushed.

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Her statement today was about redressing that situation - to replace the imagery of a stunned prime minister almost frozen in the headlights, to one composed at a podium, making a statement loaded with calmly-delivered anger.

Speculation that she could announce she was suspending the negotiations or preparing to change her position were unfounded.

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Instead she dug in - firstly on the fact she views her Chequers plan as the only viable option for an economic relationship with the EU that respects the referendum, and secondly on her refusal to countenance any backstop arrangement for the Irish border that would separate Northern Ireland from the rest of the UK.

These are arguments and positions the EU well knows.

The point of the statement was to underline just how much she means it, and to say that if the EU think she can be shifted on either position "they are making a fundamental mistake".

The statement will likely go down well with those domestically who want to see the prime minister take a tougher line with Brussels, and may even reassure some in her party who were wavering over whether Salzburg had been the final blow to the credibility of her leadership.

The first reaction from Jacob Rees-Mogg, chairman of the Brexiteer European Research Group (ERG) on the Conservative backbenches, was to welcome the prime minister's "steely resolve" in standing up to "the EU bullies".

But if the immediate question over the legitimacy of her leadership in eyes of the ERG was dealt with by this statement, the wider issue of their demand for her to dump the Chequers plan remains very much live.

Whether the defiant tone will do anything to shift attitudes in Brussels to end the impasse is far less clear.

The reaction from the EU to the suggestion their Salzburg rebuff was an "ambush" has been to say it was nothing they hadn't said before.

Their reaction to the prime minister's accusation that they are not negotiating seriously and her demand they put forward alternative proposals that acknowledge her positions could well be met with a similarly dismissive tone.

But while tone matters, so does substance.

In addition to the prime minister's attempt to reassert herself were two clear signs she is not yet prepared to walk away from the process.

First, the suggestion the UK was preparing to reformulate its vision for an Irish border backdrop, hinting at accepting regulatory alignment where it is approved by the Northern Ireland Executive and Assembly.

Second, the unilateral guarantee of the rights of around three million EU citizens living in the UK in the event of a no-deal scenario.

The aim of these comments is to make clear that despite her anger at the way she was treated in Salzburg, she believes there remains a prospect of a deal.

But it's only a prospect, and no deal will be the consequence of a failure to take her seriously.