Penal reformers say there is an urgent need to determine the nature and scale of sexual abuse in prisons in England and Wales in the wake of estimates that hundreds of inmates are being raped or sexually assaulted every year.

The figures come from the commission on sex in prison set up by the Howard League for Penal Reform, which says that survey evidence from prison inspectors estimate that 1% of prisoners are sexually abused by other inmates or staff. This implies that between 850 and 1,650 prisoners could be victims of sexual attacks every year.

Ministry of Justice data shows that the number of officially recorded sexual assaults in prison is now at its highest level since at least 2005, with 170 recorded in 2013 – up from 113 the previous year. However, the real figure is believed to be much higher and the problem has been described by the prisons ombudsman as "a hidden issue in a hidden world". Recent research in the US, where the problem is taken more seriously, shows a high level of under-reporting.

The commission, which is made up of former prison governors, academics and health experts, has found there is only very limited research on sexual abuse in jails in England and Wales and that much sexual violence goes under-reported, so the nature and full extent of the problem is not known.

The commission was blocked by the justice ministry from interviewing serving prisoners, but ex-inmates told them that the prevailing "hyper-masculine and homophobic" culture on the main wings of most male prisons made it very difficult to report assaults.

One former inmate called John told the commission: "People who are sexually assaulted or raped in prison are very unlikely to say anything because they are too scared, have been traumatised and will be bullied and victimised if they do so. Especially in YOIs [young offender institutions] where there are many, many jails that do not have VP [vulnerable prisoner] wings in order to keep vulnerable prisoners safe."

The commission was told that some prisoners traded sex for tobacco or other contraband items such as drugs or alcohol. Others used sex to settle transactions or debts with prisoners when they have no other means of paying.

Another former inmate, James, wrote in evidence to the commission: "In the past three months I have witnessed a prisoner grooming and coercing at least two prisoners into sex and buying them things in the canteen or knowing there [sic] low on tobacco, bulk buying and then saying to the person who is low on the item if you do me sexual favours then I'll give you some tobacco."

Another, William, said coercion existed: "Offers of tobacco in exchange for quick sexual gratification does occur and is sometimes taken up by those in need. Sometimes sexual abuse also occurs."

The commission's briefing on the issue says that official investigations into sexual assaults can be slow and the police are not routinely notified about allegations of abuse.

Chris Sheffield, commission chair, said: "There is an urgent need to determine the nature and scale of sexual abuse in prisons in England and Wales. The issue is treated seriously in the US, where the government has taken major steps to recognise the problem and prevent abuse.

"Despite the limited research available here, what findings we do have suggest there are disturbing parallels between the experiences of prisoners in the US and prisoners in England and Wales."

The prisons minister, Andrew Selous, however, insisted that sexual relations between prisoners were not common place: "We do not condone sex in prisons or believe that prisoners in a relationship should share a cell. Reported incidents of sexual assault in prison are rare," he said. "Where an alleged sexual assault is reported or discovered it will be investigated and reported to the police if required. We continue to work hard to understand the reasons for the increase in assaults, including sexual assaults."

Sealous added that a comprehensive review of the management of violence, including sexual violence, in prisons was under way and a new approach to investigating such crimes was being developed with the police and crown prosecutors.