MPs from all the major parties will argue that abortion should be provided on the NHS in England for Northern Irish women, in an amendment to the Queen’s speech which supporters said would act as a warning to Downing Street about the implications of a pact with the Democratic Unionist party.

The amendment, coordinated by the Labour MP Stella Creasy with the support of the Conservative MP Sir Peter Bottomley, asks the government to consider legislating so women from Northern Ireland have NHS abortion provision when they travel to England to terminate a pregnancy.

The DUP, with whom Theresa May is seeking an agreement to support her minority Conservative government, has historically taken a hard line on abortion, and Northern Ireland has some of the most restrictive abortion laws in Europe.

This month the supreme court ruled that women from Northern Ireland were not entitled to free access to abortions on the NHS, a judgment that coincided with talks beginning on a supply and confidence agreement between the Conservatives and the DUP – which are still deadlocked.

No deal has yet been reached by the Conservatives with the DUP, but Creasy, the MP for Walthamstow, said parties needed assurances not only that any pact with the DUP would not affect current equalities law, but that it would not tie the government’s hands when future legislation was needed.

“In this parliament it is not just a matter of whether hard-won progress on issues like inclusive sex and relationship education or access to services for same-sex couples will be under attack by this coalition, but also what issues don’t get addressed and are ignored,” she said.

“It is vital we do not let the fight for equality be sidelined, as it is clear without action Northern Irish women will pay the price for the government doing a deal to stay in power.”

Among those who have signed the amendment as well as Creasy and Bottomley are the SNP’s Alison Thewliss and the Green party’s co-leader, Caroline Lucas. It has also been signed by 20 Labour MPs, including the former home affairs select committee chair Yvette Cooper, Jess Phillips, Liz Kendall, Diana Johnson and Alison McGovern.

Other progressive Conservatives initially expressed discomfort at the talks, citing the DUP’s record on same-sex marriage and abortion, but May told MPs the party would not have influence on Tory social policy.

The amendment is unlikely to gain enough traction to pass through parliament but MPs hope it will serve to galvanise parliamentarians concerned about the impact of a deal with the DUP on women’s rights.

Creasy said MPs were still concerned that any changes to the law, including changes responding to the supreme court judgment on abortion, might be hostage to a deal with the DUP.

“How can it be right that if a Northern Irish woman comes to England and needs her appendix out, as a UK taxpayer we don’t charge her, but if she needs an abortion we do?” she said.

“Challenging the government’s decision to continue charging women for this service isn’t about the ability of the Northern Irish assembly to make decisions on matters like abortion rights, but how we treat all our citizens fairly when they are here on our shores.”

The amendment, which echoes the wording of the supreme court judgment, says the house “respectfully regrets that measures to address the inequality in treatment of women from Northern Ireland with regard to healthcare provision were not included in the gracious speech”.

The amendment says the current position “risks the continuation of an unwanted pregnancy which may cause distress or illness to the patient concerned purely on the basis of her place of residence within the UK rather than any medical requirements”.

The Department of Health is asked to consider legislating to ensure all UK citizens including those from Northern Ireland “may access medical services including abortion procedures in England if they so wish without charge and that such provision does not interfere with decisions made by the Northern Ireland assembly with regard to the provision of such services in Northern Ireland”.

Amendments which will be voted on along with the Queen’s speech will be chosen next week. Another cross-party amendment has been put forward by Lucas on rights of EU citizens, signed by Labour’s Chuka Umunna and several more Labour and SNP MPs. Labour’s frontbench is expected to put forward several more amendments, which could include scrapping the bedroom tax and the public sector pay freeze.