The government's independent adviser on rape has called for far greater transparency over how people who allege sexual offences are treated in the criminal justice system in England and Wales, saying the debate stirred by high profile cases must "pull back the curtain" on what happens during investigations and trials.

Prof Katrin Hohl, who advised ministers on an overhaul of how police forces and the Crown Prosecution Service handle rape, told the Guardian the government should use the public awareness generated by Russell Brand's conviction for rape to examine the use of rape myths and jury directions in trials.

"So many things are going wrong in our justice system when it comes to the treatment of victims of rape and sexual assault, but most of the time no one ever finds out what has happened during the investigation process or during a trial," she said.

Hohl said police forces and the CPS had made "significant progress" under Operation Soteria, which directs investigators to focus on suspects rather than victim behaviour, but that the court system was being left behind. A report she published last month found that cases prepared under the new system faced "a cliff edge" when they reached trial, potentially coming up against practices such as the use of rape myths by defence barristers.

"We essentially know very little about how rape and sexual assault cases play out in England and Wales and it is time to pull back the curtain," Hohl said. "We need proper research into the actions of barristers, judges and juries during trials so that victims can actually get the justice the law says they should achieve."

Her remarks follow a call from the victims commissioner, Claire Waxman, for a new legal duty on judges to direct juries whenever rape myths have been ventured during a trial. "Justice must be grounded in evidence, not misconceptions," Waxman said.

Brand was sentenced to more than 10 years in prison after being found guilty of raping one woman and sexually assaulting three others. During the trial his barrister, Ian Winter, said Brand's accusers had not "resisted or screamed or even tried to leave".

Government ministers are also understood to be considering calls for a "staggered" consent law, which would make it illegal for adults over a certain age to have sex with 16- and 17-year-olds, after a woman who alleges she was raped by Brand when she was 16 launched a campaign for the law to be changed. Mia Latter, who says she was in an abusive three-month relationship with Brand when he was 30 and she was 16, told the Sunday Times: "I think we all sort of agree that .. adults shouldn't be allowed to have sexual relationships with children, with somebody under the age of 18. That really doesn't seem like a gigantic leap to take."

On Sunday, the work and pensions secretary, Pat McFadden, told the BBC's Sunday with Laura Kuenssberg that questions over a staggered age of consent have "been raised and will be discussed", adding: "[I] can't tell you what the conclusion of that would be, but the last week has certainly put that up in lights."

Support services say demand has surged since the conviction. Ciara Bergman, chief executive of Rape Crisis England & Wales, said calls to the 24/7 rape and sexual abuse support line had quadrupled since the start of the month, while rape crisis centres were reporting a massive rise in demand. She said callers included people reminded of their own experiences, people retraumatised by the coverage, and people now questioning predation or exploitation they may have experienced at vulnerable times. Many women are also reassessing past experiences with older men, she said, after separate allegations were made public that David Walliams preyed on young women for sex. Earlier this week it emerged that the Metropolitan police are looking at "serious" sexual offence allegations against Walliams after an investigation by the Guardian and ITV News; one woman described an alleged encounter with him when she was 15 as "sexual assault". Walliams denies any wrongdoing. Bergman echoed calls for greater transparency in trials, and said the response to recent stories left "no question about the need for more comprehensive support and more rape crisis centres so victims and survivors can get the justice they deserve".