Theresa May has issued a fresh plea to Conservative MPs to unite and deliver on Brexit, urging her party to “move beyond what divides us” and sacrifice “personal preferences”.

The prime minister’s rallying cry follows another tumultuous week in Westminster that saw tensions in the Tory party reach boiling point, with one of her ministers accusing his Eurosceptic colleagues of “treachery”.

May, in a letter to all 317 Conservative MPs after her Brexit plans suffered another humiliating Commons defeat on Valentine’s Day, said the result was “disappointing” but vowed the government would continue its work to secure changes to the Irish border backstop.

She announced that she will return to Brussels for further talks with European Commission president, Jean-Claude Juncker, next week, and revealed plans to speak to the leaders of every EU member state over the coming days.

Meanwhile, Brexit secretary, Stephen Barclay, will meet the EU’s chief negotiator, Michel Barnier, on Monday to discuss the proposals of the “alternative arrangements working group” of Tories, who have been seeking a compromise solution to avoid the need for backstop.

The attorney general, Geoffrey Cox, will set out what changes would be required to eliminate the legal risk of being indefinitely trapped in the controversial Irish backstop in a speech on Tuesday.

May thanked MPs who supported the government in Thursday’s Commons vote despite rejecting the withdrawal agreement last month, saying they had shown a “determination to find a way forward for our country”.

“It is also encouraging that our confidence and supply partners the DUP voted with the government last week,” she added.

In an appeal for unity 41 days before Britain’s scheduled departure, May said: “History will judge us all for the parts we have played in this process. I believe that a country with our innate strengths, enviable resources, and enormous talent can face the future with confidence that our best days lie ahead. But we stand now at a crucial moment.

“I do not underestimate how deeply or how sincerely colleagues hold the views which they do on this important issue – or that we are all motivated by a common desire to do what is best for our country, even if we disagree on the means of doing so.

“But I believe that a failure to make the compromises necessary to reach and take through parliament a withdrawal agreement which delivers on the result of the referendum will let down the people who sent us to represent them and risk the bright future that they all deserve.”

She continued: “Without a withdrawal agreement we risk a combination forming in parliament that will stop Brexit altogether, whatever the long-term consequences for trust in our democracy.

“Alternatively, the UK might exit the EU without a deal or an implementation period. That would cause disruption to our economy and to people’s daily lives, damaging jobs both at home and across the EU.

“Instead, our party can do what it has done so often in the past: move beyond what divides us and come together behind what unites us; sacrifice if necessary our own personal preferences in the higher service of the national interest; and rise to the level of events in a way that restores the faith of the British people in our political process.”