Labour MPs will increase the pressure to end Northern Ireland’s highly restrictive Victorian-era abortion laws this week in a series of Commons votes designed to push the UK government into action.

Diana Johnson, the Hull North MP, will introduce a backbench bill on Tuesday calling for a repeal of the 1861 Offences Against the Person Act, which criminalised any woman seeking an abortion with a theoretical maximum term of life imprisonment.

Though the act was superseded elsewhere in the UK, it remains the law in Northern Ireland, forcing women to come to Britain to have abortions.

In England and Wales the 1967 Abortion Act permits an abortion in certain circumstances with the approval of two doctors. But it overlaps with the 1861 act, and Johnson says any woman purchasing abortion pills online is theoretically breaking the Victorian law.

Johnson said her 10 minute rule bill would give MPs their first chance to vote on the abortion law in Northern Ireland since a May referendum overturned a ban in the Irish Republic.

The UK supreme court indicated in June that Northern Ireland’s abortion legislation was incompatible with human rights, although judges did not strike down the law on a technicality.

Johnson hopes that her bill will win enough support to force Theresa May to act, although there is no chance it will become law because the government will not give it parliamentary time. “I want to keep up the pressure on the government to allow MPs to have a proper vote,” Johnson said.

The anti-abortion pressure group Both Lives Matter said a poll it had commissioned showed that 66% of women in Northern Ireland did not want Westminster to impose abortion laws on the region. A spokeswoman called Johnson’s intervention “an unacceptable and irresponsible attempt to override devolution in Northern Ireland and to impose abortion laws on the Northern Irish people”.

Ministers are also reluctant to allow Westminster to impose its will on Northern Ireland, even though the Stormont assembly has not sat since the beginning of 2017, and the DUP, which props up May’s government, remains hostile to any loosening of the abortion laws.

A similar abortion bill brought by Johnson in the last parliament secured 172 votes to 142, but this bill excluded Northern Ireland, as the Labour MP feared the issue was too politically charged.

Ministers are not expected to vote but Johnson’s bill has cross-party support from the Tories Sarah Wollaston and Nicky Morgan, Labour’s Jo Stevens and Stella Creasy, and other Liberal Democrat,Plaid Cymru and Green MPs.

If Tuesday’s vote is successful, Johnson is expected to lay down an amendment to halt the Northern Ireland bill on Wednesday – which is aimed at giving officials greater powers in the absence of a Stormont assembly – on the grounds that it does not set out a clear path to dealing with abortion laws.

Creasy and her fellow Labour MP Conor McGinn have put down an amendment to the bill asking Karen Bradley, the Northern Ireland secretary, to “make provision” for repealing the 1861 law. But it is not clear if the amendment will be selected for debate and Commons clerks have expressed concern to Labour MPs that it is not relevant to the legislation.

A spokesperson for the UK government said: “This legislation is required to provide the Northern Ireland civil service with the certainty and clarity they need to continue to deliver public services in Northern Ireland. Amendments will be considered by the Commons in the normal way.”