Women who make reports of inappropriate behaviour must have “confidence that they will be taken seriously”, the Prime Minister has said.

Sir Keir Starmer said politicians should be ready to put in place “mechanisms” that would instil that confidence, after a Labour MP asked him about “women of a certain age”, reflecting comments for which broadcaster Gregg Wallace has apologised.

Alison Hume (Scarborough and Whitby) asked at Prime Minister’s Questions: “Given that a significant number of members in this place are, regardless of class, ‘women of a certain age’, would the Prime Minister agree with me that when a woman of a certain age, or indeed any woman of any age from any background, says they have experienced sexual harassment or inappropriate behaviour, they should be listened to, supported and the perpetrator dealt with?”

Sir Keir replied: “I certainly agree with that and I think everybody across the House would.

“She’s right because one of the greatest barriers that women face when coming forward and reporting unacceptable behaviour in the workplace is having confidence that they will be taken seriously.

“And that requires all of us to put in place mechanisms and arrangements to make that possible.

“Everybody should be treated with dignity and respect and I’m proud of the fact that the Employment Rights Bill we are passing will strengthen protections from sexual harassment at work.”

The BBC has pulled two MasterChef celebrity Christmas specials from its schedule after Mr Wallace stepped away from the cooking competition – Celebrity MasterChef Christmas Cook Off and a Strictly Festive Extravaganza.

The presenter apologised on Monday for claiming in an Instagram video that complaints about his behaviour came from “a handful of middle-class women of a certain age”, and added he would “take some time out”.

He faces multiple complaints of inappropriate behaviour, originally from 13 people across a range of shows over a 17-year period, as reported by BBC News last week, which production company Banijay UK has said it is taking “incredibly seriously” amid an external investigation.

Mr Wallace said in a video posted to Instagram earlier this week: “I want to apologise for any offence that I caused with my post yesterday and any upset I may have caused to a lot of people.

“I wasn’t in a good headspace when I posted it, I’ve been under a huge amount of stress, a lot of emotion, I felt very alone, under siege yesterday, when I posted it.

“It’s obvious to me I need to take some time out now, while this investigation is under way. I hope you understand and I do hope you will accept this apology.”