A group of cross-party British MPs and international lawyers have given the government of Saudi Arabia until the end of the month to grant access to women activists who are alleged to have suffered torture in prison.

Refusal by the kingdom to allow the visit to take place will result, they warn, in the publication of a damning report from accounts compiled by human rights organisations and activists who have accused the Saudi authorities of abuse against the detainees ranging from water-boarding to sexual assault.

The group, which has formed a detainee review panel, had sent an official request to the Saudi ambassador to the UK, Prince Mohammed bin Nawwaf bin Abdulaziz, at the beginning of this month to obtain first hand testimony from 10 women who are being held in a number of jails in the country.

If there is no positive response by 29 January, they say, then a report will be published soon afterwards with details of allegations of mistreatment. Failure to cooperate with the investigation would be a clear indication, say activists, of an admission of culpability by the Saudi authorities.

The Saudi government has repeatedly denied the claims of mistreatment of the detainees.

Speaking at a meeting in the Houses of Parliament, three members of the panel, the Conservative MP Crispin Blunt, former chair of the foreign affairs select committee; Liberal Democrat MP Layla Moran; and Paul Williams, the Labour member of the health and social care committee, wanted to stress that they were prepared to keep an open mind and listen to the Saudi government’s case on the issue.

But it was imperative, they stressed, that they are allowed to carry out their inquiries in Saudi Arabia.

“If that does not happen then we will have to publish the report based on other sources including organisations like Human Rights Watch and Amnesty International”, said Mr Williams.

Mr Blunt had faced criticism in the past for backing British arms sales to Saudi Arabia and supporting the war being waged in Yemen by the Saudi-led coalition. He had also declared that Britain was “right to roll out the red carpet” for the visit of the Saudi Crown Prince, Mohammed bin Salman, last year.

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Mr Blunt commented: “One can say that it was my support for arms sales to Saudi Arabia that cost me re-election as chair of the foreign affairs committee. The Saudi government should be reassured that there is someone like me on the panel. It should show that they will get a fair hearing.”

Riyadh needs to demonstrate, Mr Blunt added, after the “catastrophe” of the murder and dismemberment of the journalist Jamal Khashoggi, by Saudi officials at the Kingdom’s consulate in Istanbul, that it was not mistreating opponents.

The panel will be focused on the allegations of torture and not the broader issues of the Saudi legal system. However, Mr Blunt said “it was a matter of regret” that a reform programme under which “the British Ministry of Justice was working with the Saudi ministry was stopped by Michael Gove when he was secretary of state for the prison service.”

Ms Moran said the panel will not broaden their probe into such matters as the time period the activists being held in prison without trial, pointing out that “the UK too practices indefinite detention”.

But, she continued: “We need to find out what is happening to these woman, these are very serious allegations of abuse. I am a woman and an activist, I think these women in prison would relate to me. The Saudi government should allow us this visit.”

Saudi ministers, meanwhile, maintained that the climate of international censure over the Khashoggi affair was dissipating. A number of heads of governments and multinationals pulled out of an international business conference in Saudi Arabia at the time of the murder.

But Saudi economy minister, Mohammed Al Tuwaijri, said at the Davos economic forum on Thursday that, “On a day to day basis Saudi Arabia is business as usual. Our job as government is to make sure infrastructure, legal in particular, is stable. This transformation journey, hopefully, will attract investors.”

Among political and economic leaders, the Swiss President Ueli Maurer wanted to stress “We have long since dealt with the Khashoggi case ... We have agreed to continue the financial dialogue and normalise relations again.”