The figures emerged from a three-year research project by academics at the University of Kent at Canterbury and a psychologist from Bexley Health Authority who studied cases in South East Thames Regional Health Authority. The results, first published in March, were extrapolated to give figures for the whole of the United Kingdom.
The cases involved abuse by family, carers and staff at homes and hospitals and by other residents. One of the authors, Hilary Brown, a senior lecturer in mental handicap, believes many cases of sexual abuse go unreported.
There are no estimates for the number of mentally handicapped people who are victims of physical abuse or neglect.
People First, an organisation run by and for people with learning disabilities, estimates that about 60 per cent of people who contacted its 200 local groups had been victims of physical or, most commonly, sexual abuse.
The charity Voice, which runs a telephone helpline and legal advice service for mentally handicapped people who have been abused, recorded 785 cases and referrals between September 1993 and February 1994 alone.
Julie Boniface, who founded the charity after her daughter was sexually abused in a residential home, says about 75 per cent of cases involved sexual abuse, some including physical assaults.
But in the three years since Voice was launched, only six cases have gone to court, largely because the police and Crown Prosecution Service are reluctant to prosecute when the victim or witness is mentally handicapped.
One of the charity's successful prosecutions involved a residential home in Wiltshire where a male member of staff sexually and physically abused up to 30 residents. He was jailed for three years.
Lydia Sinclair, legal adviser to Mencap, recently met Crown Prosecution Service staff to try to change the system to make it easier for people with learning disabilities to give evidence in court.
Suggestions include moves already associated with children, such as allowing witnesses to give evidence from behind a screen or by video link.
Ms Sinclair said police and courts often did not understand that having learning difficulties did not make a witness unreliable.
She and many other professionals and charities believe the abuse of mentally handicapped adults is widespread but remains hidden, partly because victims find it difficult to report assaults, and staff fear to speak out.
Ms Sinclair said: 'Enough scandals have come out of the woodwork to suggest these are not isolated cases. The Buckinghamshire case would never have come to light if the county council's internal report had not been leaked.
'If that level of cover-up can go on, involving that level of abuse, you have to ask what's happening elsewhere.'
Robin Sequeira, director of social services in Dorset and spokesman for the Association of Directors of Social Services, said most departments had written or were working on policies to protect adults at risk of abuse, including mentally handicapped people. These should include advice and guidelines for staff on how to identify and handle abuse cases.
He blames the problems on the increase in the number of privately-run homes.
Social services departments issue licences to run homes and have a duty to inspect them at least twice a year, but he argues the Government must do more to regulate and monitor the staff who work in them.
The association and social workers' professional bodies are trying to persuade the Department of Health to establish a national social services council which would keep a register of people working in residential care homes, supervise their training and regulate standards of care.
Ann Craft, who lecturers at the University of Nottingham Medical School on sexuality and sex education of handicapped people, also believes abuse is widespread but undetected.
She is director of the recently formed National Association for the Protection from Sexual Abuse of Adults and Children with Learning Disabilities which has produced a book, It Could Never Happen Here, advising professionals on prevention and treatment.
She believes social services departments should be considered negligent if they fail to adopt procedures for staff to identify and counsel people at risk.
Mencap is conducting a survey to establish the scale of abuse so that it can campaign for better guidelines for local authorities.
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