A psychiatric nurse has made fresh allegations of rape against Jimmy Savile while he worked at Broadmoor hospital, claiming a former patient told her she had been repeatedly abused by the TV star while she was confined to the hospital during the early 1980s. Twelve police forces are now passing allegations to the Metropolitan police, which is looking into sexual abuse claims against the late presenter.

Naomi Stanley, a psychiatric nurse now based in Brighton, said one of her former patients, a young woman, told her she had been raped repeatedly by Savile near and under the stage of the theatre of the high-security hospital, but when she had threatened to report him, "he laughed in her face, and said that nobody would believe her and he could do what he liked".

"She described him as being 'very forceful' and treating her like she was an animal, like a piece of shit, like he had no regard for her whatsoever," Stanley said. "She felt horribly abused, it was not consensual sex, she was very keen to stress that at the time. And I believed her. There was no doubt in my mind that she was extremely distressed and upset by it." The woman said the abuse stopped only when Savile moved on to abusing other younger women at the hospital.

The allegations are the latest in a torrent of fresh abuse claims against Savile, whom the Metropolitan police described this week as a predatory sex offender who abused children and young women on a national scale. Stoke Mandeville hospital and Leeds General Infirmary, with which Savile also had close ties, have also become the subject of allegations of serious sexual abuse of young women, following accusations linked to the BBC, Duncroft approved school in Staines, the Haut de la Garenne children's home in Jersey and elsewhere.

The BBC was criticised by Tory party chairman Grant Shapps. "It seems unimaginable that the people in the BBC didn't know," he said on BBC1's Question Time. Shapps questioned the decision to air tributes to Savile last Christmas "after it was already known at senior levels within the BBC that something was wrong, enough to have had a serious Newsnight programme made about it and enough to raise serious concerns".

The Labour leader, Ed Miliband, said every institution that had links to Savile should carry out "the most far-reaching investigation of what happened, who knew what, when, about what was happening in that institution and why nothing was done about it".

One of the country's leading child protection experts, the former head of the Child Exploitation and Online Protection Centre, Jim Gamble, said the independent inquiry set up at the BBC should be broadened to include every institution with which Savile had connections.

Savile, who died last October, worked at Broadmoor as a volunteer for almost 40 years, describing himself as the "honorary assistant entertainments officer". He had an office and living quarters at the hospital and was given a personal set of keys to the wards, West London Mental Health Trust, which now runs the hospital, said on Thursday. It confirmed the hospital has a theatre area, adding "the design has been radically altered since the 1980s and it is not clear now if there was any space beneath it".

Stanley, who has more than 30 years' experience in nursing, said the woman made the allegations in the early 1980s, shortly after she was transferred from Broadmoor to another psychiatric hospital in the south of England. Stanley said she had been very distressed by the woman's account, which she found entirely credible, and had reported it at the time to her superiors and to police officers involved in the patient's supervision, but no further action had been taken. The Guardian is not naming the hospital to protect the patient's identity.

The current management of the second hospital and the police force concerned said their records did not date back to that time, but that any allegations would have been passed to Thames Valley police, which oversees Broadmoor. On Thursday, Thames Valley became one of 12 police forces to confirm it had received allegations of abuse relating to Savile. The force said it had passed three complaints to Scotland Yard, which is co-ordinating the inquiry. The other forces are North and South Yorkshire, Sussex, Surrey, Greater Manchester, Tayside, Cleveland, Jersey, Northamptonshire and Lancashire.

Separately another former Broadmoor patient, a young girl at the time but now living as a man following a sex-change operation, said Savile had reached under his nightie and groped his breasts while he was watching TV with other young girls. Steven George, at the time a 17-year-old girl called Alison Pink, told the Sun: "It's staggering to think Savile was given the run of Broadmoor … He could access any of the girls' bedrooms."

One woman who was a patient at Leeds General infirmary in 1972 said she saw Savile abuse someone she thought was a girl who was brain-damaged. June Thornton was incapacitated while recovering from a back operation at the time and said she was ignored when she told a nurse about the abuse.

"I thought he was a visitor coming to see her. He started rubbing his hands down her arms and then, I don't know of a nice way to put it, but he molested her. He helped himself. She just sat there and couldn't do anything about it," she told ITV News.

Another woman said she was assaulted by Savile at the age of 13 while being treated for spinal injuries at Stoke Mandeville in 1971. Caroline Moore, from Clarkston, East Renfrewshire, who is paralysed from the chest down and uses a wheelchair, told the Daily Mail that Savile had "leant down and I was excited because I thought he was going to give me a wee peck on the cheek. But he took my face in his hands and rammed his tongue down my throat".

Gamble said there was a "positive cascade" of allegations coming forward against Savile. "What happens is that people who have held on to the secret see that this is being treated seriously, realise the secret has been a burden throughout their young and later lives and see that there is now an opportunity to come forward and be heard and that it will be cathartic to do so.

"The speed with which information is now coming in to the Metropolitan police means they will be being inundated with fresh pieces of information. It will be extremely difficult for them because they don't have a live suspect, they don't have a crime scene and the outcome from this inquiry is not going to be criminal with regards to Jimmy Savile.

"What is needed is a broad review to re-establish and reinforce victim confidence. It needs to be wide ranging and not just within the BBC. There is an opportunity to carry out a review that actually creates a positive outcome for all of this, to allow the institutions involved to reinforce the pathways for people to report wrongdoing in the future and to enable each of these institutions to reflect on what went wrong and be reassured that they have everything in place to ensure nothing like this happens again."

West London Mental Health Trust said it was shocked at the allegations of abuse at Broadmoor and would co-operate fully with the police, although it had not received any direct complaints.

"These allegations relate to a time when Broadmoor was a separate, somewhat isolated organisation, not part of a wider NHS trust. Procedures and protocols, notably security arrangements, have changed significantly in the past decade to reflect that different culture."

• This article was amended on 12 October 2012. The original version stated that 12 police forces were investigating claims against Savile. In fact, 12 police forces are passing allegations to the Metropolitan police, which is investigating.