MPs are to try to outlaw the courtroom murder defence of “rough sex gone wrong” during parliamentary debates on the domestic abuse bill, as cases of domestic violence soar during the coronavirus lockdown.

The repeatedly delayed legislation came before MPs on Tuesday amid calls for a specific ban on “non-fatal strangulation”, and threats of legal action over the provision of accommodation for domestic abuse survivors during the pandemic.

The government has promised to look at what has been called the “fifty shades” defence to murder during sex, but has not yet announced any detailed legislative wording to introduce a ban.

An amendment backed by the Labour MP Harriet Harman and the Conservative MP Mark Garnier is likely to be the focus of efforts to prevent anyone charged with murder escaping justice by alleging that the victim had consented to sex games.

Harman urged MPs in the Commons on Tuesday to “stop this injustice” of the sex game defence, which means a man who admits to causing injuries that kill a woman “literally gets away with murder”.

“This is a double injustice. Not only does he kill her but he drags her name through the mud. It causes indescribable trauma for the bereaved family who … see the man who killed her describe luridly what he alleges are her sexual proclivities. She of course is not there to speak for herself. He kills her and then he defines her.”

The justice secretary, Robert Buckland, told MPs the government hoped to present a solution to end the “rough sex defence” by the report stage of the bill but did not disclose any details.

The campaign to change the law has been led by the organisation We Can’t Consent to This which has calculated that more than 20 women a year are injured or killed when it is claimed that sex games have gone wrong.

The organisation also supports a call by the Centre for Women’s Justice (CWJ) for MPs to include a new offence of “non-fatal strangulation” in the domestic abuse bill.

Harriet Wistrich, the director of the CWJ, said: “Offenders are getting away with little or no punishment for this terrifying and dangerous offence. Police and prosecutors are not taking this offending sufficiently seriously. A simple amendment to the domestic abuse bill, making non-fatal strangulation a specific serious offence, could provide a remedy and help reduce femicide.”

The bill also contains clauses requiring domestic abusers to take polygraph tests – commonly referred to as lie detector tests – on release, and regulations to ban perpetrators from cross-examining victims during family court proceedings.

The new attorney general, Suella Braverman, told the Commons extra funds were being made available to frontline services dealing with victims of domestic abuse during the coronavirus crisis. She reminded those in danger that “they will not be breaking the law if they flee their home [during the lockdown] and seek help outside”. MPs were also told that police in London are making 100 arrests a day in relation to domestic abuse cases.

A survey published by Women’s Aid on Tuesday found that more than two-thirds of survivors said domestic abuse was escalating under lockdown, with 72% saying their abuser had more control over their life since the Covid-19 crisis.

More than three-quarters (78%) of survivors, the survey found, reported that Covid-19 had made it harder for them to leave their abuser.

In a related development, Southall Black Sisters and the Public Interest Law Centre are launching a legal challenge against Robert Jenrick, the housing, communities and local government secretary, –for the department’s “failure to provide emergency funding for adequate accommodation for domestic abuse survivors during the Covid-19 crisis”.

The organisations said: “Between 23 March and 12 April 2020, the number of recorded killings of women rose from a weekly average of two deaths per week to an average of five deaths per week, a total of 16 killings within a three-week period.

“During lockdown, the Metropolitan police have arrested an average of 100 people a day for domestic abuse-related offences and have received a 30% rise in domestic abuse calls.”

A government spokesperson said: “Our [domestic abuse] bill will better protect victims, making sure they have the support they need whilst more offenders are brought to justice. We have committed to ensuring the law is clear that this [rough sex] ‘defence’ is unacceptable and are looking at ways to achieve this.”

The government has pointed out that those who deliberately cause harm or injury during sex can already be convicted under existing laws.