Kate Maltby, who claims Damian Green made inappropriate advances to her, says she told a senior Downing Street aide about his behaviour in 2016.
The MP, who denies the claims, was sacked from the cabinet on Wednesday.
This came after an inquiry found he had broken the ministerial code over “misleading” statements after pornography was found on his computer.
Prime Minister Theresa May said she was not aware of the claims about Mr Green until last month.
Speaking on a visit to Cyprus, she said she had first read about them in an article by Ms Maltby in the Times newspaper.
She said: “I recognise that Kate Maltby was obviously extremely distressed by what happened. Damian Green has recognised that and he has apologised. I think that is absolutely the right thing to do.”
She has said it is important that people working in Parliament feel they can bring forward any concerns they have to be “treated seriously”.
The Cabinet Office investigation into Mr Green was prompted by her allegations that Mr Green had “fleetingly” touched her knee in a pub in 2015, and in 2016 sent her a “suggestive” text message.
The inquiry was later widened to include the claims about legal pornography being discovered on his computer after a police raid on his Commons office in 2008.
Speaking after the inquiry, which concluded that her evidence was “plausible”, Ms Maltby told the BBC she had not told many people about the alleged incident at the time – except her parents – as she “wondered if it was a one-off”.
“Eventually I spoke to a very senior and long-serving aide of Theresa May,” she added.
When giving evidence to the inquiry, she told its head, Sue Gray, that Downing Street was aware of her allegations “to the best of my knowledge”.
“I was aware that he was the deputy prime minister and I was aware that No 10 knew about it.”
‘Story about power’
Ms Maltby said she had never called for Mr Green’s sacking, but wrote her article because she wanted to change the culture of Downing Street.
“This whole story has been about power,” she said. “Damian Green became a very, very powerful person.
“I was aware that there seemed to be improper mixing of mentorship and sexual advance within the Conservative party in his case.”
Ms Maltby added: “My actions in this have never been guided by the quest to claim scalps, to force resignations to end people’s careers.
“We need an end to the era in which the sexual exploitation of younger people is the sort of peccadillo of a politician.
“That is tolerated by those in power and perhaps exploited to enforce party discipline but not to actually do any good.”
A Downing Street source told the BBC: “The Cabinet Office conducted a thorough investigation into a number of allegations about Damian Green.
“The PM has made it clear that everyone should be able to work in politics without fear or harassment – that is why she has brought forward a new code of conduct for the Conservative Party, and set up a cross-party working group to make recommendations about the Houses of Parliament.”
Speaking on Thursday, Mrs May reiterated her personal “sadness” at sacking her close ally Mr Green but said it was “absolutely right” that he had apologised to Ms Maltby.
‘Concerns treated seriously’
Although Mr Green was sacked over his statements about the pornography on his computer, he used his resignation letter to also apologise to Ms Maltby, who was a family friend.
“I deeply regret the distress caused to Kate Maltby following her article about me and the reaction to it,” he wrote.
“I do not recognise the events she described in her article, but I clearly made her feel uncomfortable and for this I apologise.”
Meanwhile, former senior police officer Bob Quick and retired detective Neil Lewis, who told the BBC he had been “shocked” by the contents of Mr Green’s office computer, are being investigated for possible breaches of the Data Protection Act.
The Metropolitan Police, who referred the case to the data regulator, said the pair were under investigation over the “apparent disclosure to the media of confidential material gathered during a police investigation in 2008”.
Conservative MPs are angry about the alleged actions of the two retired detectives, with Jeremy Hunt claiming they “did not sit comfortably in a democracy” – something, he added, Theresa May “had made clear” in her letter to Mr Green.
Boris Johnson said the actions of the police “had the slight feeling of a vendetta”, and needed to be investigated further.