British defence minister Michael Fallon quit on Wednesday saying his conduct had fallen below the high standards demanded of his position, the first resignation in a sexual harassment scandal in parliament.

A growing number of women and men working in Britain's parliament have complained of inappropriate behaviour by lawmakers, largely prompted by sex abuse allegations against Hollywood film producer Harvey Weinstein.

Fallon apologised earlier this week for touching a radio presenter's knee in 2002 - something the woman in question described on social media as "mildly amusing".

In his letter of resignation to Prime Minister Theresa May on Wednesday, he said there had been many allegations about lawmakers in recent days, including "some about my previous conduct".

"Many of these have been false but I accept that in the past I have fallen below the high standards that we require of the armed forces," he said. "I have reflected on my position and I am therefore resigning as defence secretary."

May, weakened after losing her Conservative Party's parliamentary majority in a snap June election, said she appreciated "the characteristically serious manner" in which Fallon had considered his position and "the particular example you wish to set to servicemen and women and others".

May has moved swiftly after a weekend report that one of her ministers asked a female secretary to buy sex toys, the first allegation that triggered soul-searching in parliament over how junior workers are treated.

Allegations of sexual abuse have ranged from a charge of rape by an activist in the main opposition Labour Party by a senior party member, to unconfirmed details of serial "sex pests" on a list reportedly drafted by aides and researchers in parliament.

Damian Green, May's deputy in the British government, has denied an allegation that he made an inappropriate sexual advance on a young woman.

May, who has long championed the careers of female lawmakers, said earlier on Wednesday that action would be taken when there were allegations and evidence of sexual misconduct.

"I am very clear that we will take action against those where there are allegations that we see, and the evidence is there, that there has been misconduct," she told lawmakers.

- Reuters