G4S, the controversial private security company, is to run services providing medical examinations and counselling for victims of rape and sexual assault in the West Midlands.

The company has been awarded a three-year contract to take over two sexual assault referral centres (Sarcs) in Birmingham and Walsall. The national network of 33 centres across England which have developed over the past decade also allow rape and sexual assault victims to report attacks without going to the police first.

The decision to award the contract for such sensitive services to the company, despite widespread criticism over its failings in the Olympics security contract, was made by local NHS commissioners who have recently taken over responsibility for the network of Sarcs from the police.

Union leaders and violence against women campaigners sharply criticised the "sell-off" of such sensitive services to a private company with such a chequered record.

Karen Jennings, Unison's assistant general secretary, said: "It is shocking that a private, profit-making company with such a chequered record should be put in charge of these highly sensitive and intimate support services. A woman at her most vulnerable must be treated with the ultimate respect, dignity and sensitivity by trained professionals who she feels confident about placing her trust in," she said.

"The police service has developed over the years experience and expertise in working with women at such difficult times. They have well-established links with supportive services and agencies and that progress should not be undermined by selling these services off."

Rape Crisis (England and Wales) said victims of sexual violence need to access long-term support and counselling as well as immediate medical and legal help: "Our concern is that commissioning generic private contractors such as G4S to run Sarcs will lead to a focus on cost-efficiency above the needs of sexual violence victims and, in particular, that crucial long-term support services will be sacrificed in the name of cost-cutting."

The decision to give G4S the contract appears to follow complaints that the existing centre in the West Midlands had failed to meet official minimum standards for at least four years.

G4S Forensic and Medical Services is already involved in providing similar services in Essex, Worcester and Telford. Women "crisis workers" staff the centres, assist with medical assessment and provide advice on follow-up services. G4S also provides women-only call handlers for dedicated phone lines for victims who contact Sarcs in Lincolnshire, Cambridgeshire, Wiltshire and Hertfordshire. It also provides a specialist service for child victims of sexual abuse in Devon.

The company has recently advertised for "female crisis workers" to work at Sarcs at £12.50 an hour and to be on call on a 24/7 rota.

In response to the criticism, Gary Green, managing director of G4S Forensic and Medical Services, said it has been working in this area since 2005 and had developed substantial expertise in providing a high standard of care while helping the police protect the evidence they need to secure a conviction: "Our dedicated medical staff come from a range of backgrounds in health and social care and are absolutely committed to looking after the needs of the victim at what can be a very traumatic time. That's why we work with the local health services and the police to ensure that in the centres we manage, we have specially trained advocates focused solely on the welfare of those who come forward to report rape or sexual assault."

At the launch of the West Midlands G4S contracts earlier this week, Chief Superintendent Simon Hyde, the West Midlands police's head of public protection, said: "Research and evidence stresses how important it is for victims to be able to access skilled, experienced forensic medical practitioners as part of the service, and that a high ratio of these physicians should be female.

"We wanted to bring the focus back on the service we provide to victims and have ensured that we have consulted with our partners and voluntary agencies to ensure the facilities provided through the NHS give the highest standards of victim care and treatment."