Sexual harassment complaints in parliament are dealt with too slowly and opaquely, the chair of the Commons equalities committee has said, after concerns were raised over a former Downing Street special adviser.

Caroline Nokes said she believed Daisy Goodwin, who has accused Daniel Korski of touching her breast in No 10 in 2013.

Goodwin claimed she was making the allegation because Korski had trouble controlling impulses and she wanted to draw attention to his alleged behaviour given he was running to be the Tory candidate for mayor of London.

Korski pulled out of the mayoral race on Wednesday, saying he categorically denied wrongdoing but that the row had become a distraction. Nokes called for all political parties to draw up a code of conduct for future candidates.

“Women are expected to get on with the rough and tumble of politics or get out,” the Conservative MP told BBC Radio 4’s Today programme. “We need to have a zero-tolerance approach to inappropriate behaviour by men in politics towards women.”

Nokes stressed that she believed Goodwin. She said: “I think there have been all sorts of questions raised as to whether she’s telling the truth, whether she misremembered what happened. Women do not make mistakes when they know a man has touched their breast.

“I’m really disappointed that I seem to spend my time talking about the fact that I believe Daisy Goodwin.”

Political parties had about a year to draw up a code of conduct explicitly making clear that Class A drug-taking, watching porn at work and harassment were unacceptable, said Nokes.

“We’ve seen all three of those things over the course of the past 12 months and who would have ever imagined that,” she said, adding a new code of conduct should be in place by the time of the next general election.

The code should apply to people standing at all levels of public office, including councillors, she added.

Nokes said current complaints systems were too slow and opaque, and called for them to be sped up and more transparent in the interests of the alleged victims and those accused.

Goodwin has submitted a formal complaint to the Cabinet Office, but the government has yet to confirm an investigation has been launched.

In a statement on Wednesday, Korski said: “The pressure on my family because of this false and unproven allegation and the inability to get a hearing for my message of ‘the London Dream’ makes it impossible for my campaign to carry on.

“I am proud of having run a positive campaign that championed new ideas, technology and talent.”