Labour promised in its 2024 manifesto to halve violence against women and girls within a decade.
“For too long, victims of rape and serious sexual offences have felt let down by our justice system,” Burnham said.
“Prosecution rates for rape remain shamefully low, with many victims waiting years for justice. This is not good enough.”
The changes were “long overdue” and would make a “significant difference” but focusing on prosecution alone would not be enough, he added.
“So as well as ensuring victims get justice, we will step up action to prevent these horrific crimes from happening in the first place,” the prime minister said.
Nichols spoke publicly for the first time about being raped when she accused the then Justice Secretary, David Lammy, of using crime victims as a “cudgel” to push through his reforms of the legal system.
She was criticising the Courts and Tribunals Bill’s plans to limit jury trials to cases with a likely prison sentence of three years or more.
She said she had waited 1,088 days to go to court, with every day being “agony” and the “trauma” made worse by her role in public life.
Her attacker, she said, was acquitted at crown court but subsequently ordered to pay compensation after she won a civil case against him.
“It is because I have been raped that I am as passionate as I am about what it means for a justice system to be truly victim-focused,” she said.
“It is because I have endured every indignity that our broken criminal justice system could mete out that I care what kind of reform will actually deliver justice for survivors and victims of crime more widely.”
Responding to news of the specialist courts being rolled out, the Conservatives said tackling delays to criminal rape trials was “long overdue” and they pushed Labour to commit to scrapping plans to restrict jury trials.
“The fact that victims have been withdrawing their cases because they have taken too long has been a disgrace,” said shadow justice secretary Nick Timothy.
“Labour need to get courts sitting throughout the year, end the delays and clear the backlog – not undermine our right to a trial by jury.”
Last year another charity, the Salford Survivor Project, said victims of rape and sexual assault were being “failed by the system” as court backlogs reached a record high.
The long delays for cases to go to trial were having a serious impact on victims’ mental health, it said.
Also last year, a woman who says she was sexually assaulted by a taxi driver on her 21st birthday told BBC News she had dropped the case because of court delays.
She reported the alleged incident in early 2022 and gave evidence in court in December 2023 but the case was adjourned until September 2024 when the judge fell ill.
“I made the decision, even though I hate the statement, to drop the case,” she said. “I couldn’t let this hurt me further.”
The Crown Prosecution Service said that, without her testimony, the case had been dropped because of insufficient evidence.
If you have been affected by any of the issues raised in this story, information and support can be found at the BBC’s Action Line website.
