Theresa May is expected to name a new defence secretary after the resignation of Sir Michael Fallon on Wednesday.
He stood down, saying his conduct had "fallen short" of the required standards after allegations of inappropriate sexual behaviour.
BBC political editor Laura Kuenssberg said a "radical reshuffle" was not expected, but instead a "sideways move or single shuffle up".
Scottish Tory leader Ruth Davidson said the "tone of politics had changed".
Sir Michael is the first politician to quit following recently revealed claims of sexual harassment in Parliament.
He told the BBC that what had been "acceptable 15, 10 years ago is clearly not acceptable now".
Ruth Davidson said it was time to "clean out the stables" in British politics.
She told the BBC: "It isn't actually about sex. It's about power. It's always about power. And we as elected representatives have to hold ourselves to a higher standard.
"We're in positions of power so we can make things better for who comes after, not so that we can exert that power in a nefarious way."
In his resignation letter, Sir Michael said a number of allegations that had surfaced about MPs, including himself, had been false, but added: "I accept that in the past I have fallen below the high standards that we require of the Armed Forces that I have the honour to represent."
Sir Michael later told the BBC it "was right" for him to resign, adding: "Parliament now has to look at itself and the prime minister has made very clear that conduct needs to be improved and we need to protect the staff of Westminster against any particular allegations of harassment."
When asked if he thought he should apologise, Mr Fallon said: "I think we've all got to look back now at the past, there are always things you regret, you would have done differently."
Mrs May said she appreciated the "serious manner" in which Sir Michael had considered his Cabinet role and paid tribute to "a long and impressive ministerial career".
Laura Kuenssberg said that sources close to him do not believe he is "some kind of predator", but that he had not felt that he would be able to account for every encounter in his long ministerial career.
She said there was already a "fragile balance" in Cabinet and that the prime minister would be wary when naming Sir Michael's successor.
It was not just about appointing a figurehead for the military, she added, but with big issues like Brexit on the table, the appointment would be about "keeping the political peace."
On Tuesday, a spokesman for Sir Michael confirmed that he was once rebuked by a journalist, Julia Hartley-Brewer, for putting his hand on her knee during a dinner in 2002.
Ms Hartley-Brewer, a former political editor of the Sunday Express and regular political commentator, told BBC Radio 4's The World Tonight: "If he has gone because he touched my knee 15 years ago, that is genuinely the most absurd reason for anyone to have lost their job in the history of the universe, so I hope it is not because of that."
The BBC understands fresh claims about his behaviour were raised on Wednesday, but Downing Street refused to comment.
Factfile: Michael Fallon
- Date of birth: 14 May 1952 (aged 65)
- Job: MP for Sevenoaks, Kent, since 1997. Defence secretary from July 2014 to 1 November 2017
- Education: Privately educated at Epsom College, in Surrey; Studied classics and ancient history at the University of St Andrews
- Family: Married to Wendy Payne. The couple have two sons
- Honours: Knighted in 2016 in David Cameron's resignation honours
Labour MP Jess Phillips said recent allegations made against MPs were a cross-party issue, but said Sir Michael's resignation made her feel that action was being taken.
She added: "I am not interested in scalps, I am interested in cultural change, in parliament and in our political parties, to make it safer and a better environment for women."
Following a range of recent allegations, including claims of a lack of support for those making complaints, Mrs May has written to party leaders calling for the "serious, swift, cross-party response this issue demands".