Labour said to be considering amendments to Queen’s speech on school cuts, winter fuel allowance and the bedroom tax

The Democratic Unionist party has said it will act as a “brace against hard austerity” in its deal with the Conservatives, as rebel Tory MPs suggested that they could torpedo unpopular policies by tacitly backing Labour amendments to the Queen’s speech.

The DUP’s leader, Arlene Foster, said it was “right and proper” that her party would vote for Theresa May’s Queen’s speech next week. However, DUP sources told the Guardian on Friday that the party wanted a “more compassionate approach to austerity” in any deal.

Labour is believed to be considering tabling amendments to Wednesday’s speech on a range of issues including school cuts, preserving the winter fuel allowance, and scrapping the bedroom tax, which some Conservatives may allow to pass by abstaining on the vote.

Some Conservative backbenchers who have grave doubts about May’s leadership are keen to ensure that the prime minister feels the heat from Tory MPs in the Commons, even though they have no desire to see the Queen’s speech fail.

It is understood that DUP officials have sought meetings with opposition parties, including the Liberal Democrats, to take the temperature of amendments planned for the Queen’s speech. If the DUP’s 10 MPs are willing to support opposition amendments, that would increase pressure on Downing Street.

A DUP source told the Guardian: “The DUP is a unionist party and that means it has concerns for the people of the whole of the United Kingdom. That means protecting the winter fuel allowance for the elderly person in Scotland is as important to us as protecting the welfare of the elderly person in Northern Ireland. We are keen to defend the rights and welfare of the vulnerable across the UK and that is why any arrangement in our view should be one that benefits everyone in the UK.”

Though Conservative backbenchers ostensibly gave May their backing after the 1922 committee meeting of Tory MPs on Monday night, one former Conservative minister described the prime minister as “toast … it’s a question of when we want her to go”. Backbenchers said they wanted to remind the prime minister of how she had been “drained of all power” following the party’s dismal election campaign and the loss of her majority.

“When you have a hung parliament, power shifts from the cabinet room to the floor of the House of Commons,” one Tory MP said. “No one wants to see the Queen’s speech fail – we want to get through that.

“But if they were silly enough to put into the Queen’s speech things that don’t command support across the party, you shouldn’t be surprised to see a Labour party gleefully jump on that and put down things Tories might not be willing to oppose.”

Negotiations will continue over the weekend with a view to securing a DUP-Tory agreement ahead of the Queen’s speech. DUP sources also stressed the importance of everyone in Northern Ireland “owning” whatever concessions the party specifically wins for the region in its discussions with the Conservatives.

Facebook Twitter Pinterest Arlene Foster has assured the new Taoiseach, Leo Varadkar, that she wants a ‘sensible Brexit’. Photograph: Brian Lawless/PA

“One out of three voters backed the DUP in the election last week, but that does not mean we will not speak up at Westminster for the other two-thirds who didn’t vote for us. Any agreement the DUP secures and any of the things we can win over for Northern Ireland will be for everyone in Northern Ireland,” the DUP sources added.

Labour sources said no formal conversations had yet been had with Tory backbenchers, but said there were obvious areas where it was possible that the party could inflict defeat on the government.

“She doesn’t have a mandate for scrapping the winter fuel allowance, or taking hot meals away from children, and there could be support for other things too, such as scrapping the bedroom tax,” the source said. “Police cuts, more firefighters, prison guards – there could be a lot of agreement.”

The Lib Dem leader, Tim Farron, who resigned earlier this week but will lead the party’s response until a new leader is chosen, said their amendments would include “a clear statement about an open border for Ireland”, which could gain DUP backing.

“This is not tribal and pretty reasonable,” Farron said. “This puts the government in a tricky spot and offers us the chance to defeat them, the first time since 1924 that’s happened. Freedom of movement matters and this is a clear way the other parties can work with the Liberal Democrats.”

Former prime minister David Cameron was forced to accept an amendment to the Queen’s speech in 2015 that protected the NHS from measures in the Transatlantic Trade and Investment Partnership (TTIP) when Tory Eurosceptics, Labour and SNP MPs collaborated.

Meanwhile, Foster has assured Ireland’s new Taoiseach, Leo Varadkar, that she wants a “sensible Brexit” that works for both Northern Ireland and the Irish Republic. “We want to see a Brexit that works for everybody, not just in Northern Ireland from my perspective, but in the Republic of Ireland as well, so it is about a sensible Brexit,” she said.