When Tony Blair asked Margaret Beckett to become foreign secretary in May 2006 she was so taken aback that all could she could say to the then prime minister was “fuck”. It was not that she didn’t want the job but more that she had never thought it would be offered to her.

Beckett’s time at the Foreign Office did not last long – just 13 months – and it was far from plain sailing. It ended when Gordon Brown took over from Blair and Beckett returned to the backbenches. But whatever her successes and failures, she will go down in history as the first female foreign secretary. And the aura of parliamentary grandee has surrounded her, increasingly, ever since.

So when two Labour MPs with an idea about how to secure a second referendum on Brexit were seeking someone to speak for their campaign in the House of Commons they knocked on Beckett’s door. Peter Kyle and Phil Wilson knew she would be listened to across the chamber. “They came and said they thought they had found a way to do it,” she says.

Beckett has made no secret of her very strong feelings about May’s handling of Brexit, and of the need to put the issue back to the people. She found May terrifying. “The more I look and listen to this woman the more I think she’s capable of doing literally what she says, driving us right to the last minute, and then saying ‘it is my deal or no deal’,” she says.

“I have become increasingly worried that the house could decide something which is so far away from what people thought they were getting when they voted to leave that it could cause serious ructions. Some very strong Leavers say they don’t think people should have a second opportunity to be consulted because they might have changed their minds. That seems to me to be incredibly dangerous as well as completely indefensible.”

Beckett cannot recall any leader or prime minister behaving like May has in her more than 40 years as an MP. “This knocks every other crisis I have lived through into a cocked hat.”

Theresa May thinks she is a dictator and that she doesn’t have to discuss anything with anybody

Recalling her first ever job in government she says: “I was in the whips’ office in January 1975 during the minority Labour government … We had a nominal majority of two. My very clear recollection is that the government did not always get its way and we had to work across the house. Theresa May thinks she is a dictator and that she doesn’t have to discuss anything with anybody.”

But it is worse than that. She says May ignores the votes of a parliament in which her government has no majority. “This prime minister has actually torn up the British constitution because anything she does not like she just ignores and no one seems to be able to stop it.

“The notion that you have a government that gets defeated by the largest margin in history and just ignores it is weird. If you go back, she tried to keep parliament out of it, then she tried to stop parliament having a meaningful vote. Then having agreed to a meaningful she tried make it a meaningless vote.”

So when Kyle and Wilson came up with their idea of an amendment under which May’s deal would be allowed to pass on condition it was put to a confirmatory vote of the people, Beckett saw it as a clever idea – and a way out. It is the same model as that used to bind the people of Northern Ireland and the Republic behind the Good Friday Agreement.

“If you look at what happened in Northern Ireland, there was this horrendous, complex, difficult, tense situation with bloodshed all around it and people sat down and thrashed something out and then they said to the people ‘will this do, can you live with this balance?’ And because they could, that agreement has held through enormous difficulties and vicissitudes.”

Beckett put her name to a tweaked Kyle-Wilson plan last Wednesday when parliament held a series of indicative votes on alternatives to May’s deal and spoke up for it in the Commons. The updated version said that there should be a confirmatory referendum for any Brexit plan agreed by MPs, not just May’s. It received the highest number of votes of any of the eight options put forward for “indicative votes” although it lost by 268-295.On Monday, when MPs try to whittle down the options and find one or more that can secure a majority, it is likely to be voted on again, and Beckett will be there to urge it on. Asked if she thinks it can get the elusive majority she is cautious. “I don’t know,” she says. “I hope so.” One thing she does know is that a second referendum is a better idea than what she calls May’s “crap deal” and several other put forward by MPs which would leave the UK as a “rule taker, not a rule maker.” And above all, she says, “it is just the right thing to do.”