A Government minister has “paused” support for Daniel Korski’s bid to be London mayor after TV producer Daisy Goodwin submitted a formal complaint accusing him of groping her in 10 Downing Street a decade ago.

Education minister Claire Coutinho said the allegation is “very serious and concerning” and “if there is a complaint in the system, it needs to be followed up swiftly”.

Mr Korski has denied the “baseless” claim by Ms Goodwin, who wrote hit TV show Victoria, following an incident which allegedly took place while he was a special adviser to then prime minister David Cameron.

Ms Goodwin confirmed she has submitted a complaint to the Cabinet Office, although she said it was “harder than trying to get a telephone engineer”.

She posted a picture on Instagram showing an automatic reply to her email.

“I sent an email at 5pm yesterday saying that I want to make a complaint about Daniel Korski – and who should I speak to,” she told the PA news agency.

After reports that she had made a complaint emerged, she said she “got an email from someone in (the Cabinet Office) ethics (team) suggesting we talk – I am waiting to for that to happen!

“It’s harder than trying to get a telephone engineer.”

Appearing on BBC Radio 4’s Today programme, Ms Goodwin did not rule out making a complaint to Conservative party headquarters.

She said: “I assume that because this happened in Downing Street that I should complain to them, but I’m happy to complain to the Conservative Party as well.”

Ms Coutinho, who had previously praised Mr Korski’s “clear vision for London”, suggested her support is now on hold.

She told Sky News: “I would say I’d be on pause at the moment because lots of things are happening.”

Asked to confirm she has suspended her support, she said: “Yes, because I think we need to see what’s happened.

“But, at the same time, this is an allegation. He’s roundly denied it.

“If there is a complaint in the system, it needs to be followed up swiftly so we can find the facts and see what’s happened, but I do think it’s a very serious and concerning allegation.”

Senior Tory Robert Halfon has also reportedly suspended his support for the Korski campaign.

Mr Korski has said it is “categorically” untrue that he groped Ms Goodwin and has pledged to stay in the race to become the Conservative candidate for London mayor.

The Cabinet Office declined on Wednesday to confirm whether a formal complaint has been made.

Mr Korski used an interview with TalkTV on Tuesday to say he had met Ms Goodwin, but denied that anything improper had occurred.

“I didn’t do what’s been alleged, I absolutely didn’t do that. Ten years ago, when it happened, nothing was said to me. Seven years ago, when this first came out, nobody alleged anything to me.

“I just didn’t do what’s being alleged.

“I’ve had countless meetings in Number 10, have had thousands of meetings since then in my business career. I treat everybody with the utmost respect.

“I work hard to create an empowering and respectful environment, and I sit appropriately in chairs, and I try to treat everybody with respect in order to get the best out of a professional situation.

“I don’t know how she could have come away with that perception.

“I certainly didn’t leave the meeting feeling that I had done anything wrong, and subsequently even wrote to her, congratulating her on some of her professional success. But I don’t really know why she felt the way she did.”

In the interview he acknowledged that the allegation had been raised as part of the process for choosing the Conservatives’ candidate to become London mayor.

“During the process, I was asked about if there were any outstanding issues the party may be aware of. I said to the party, seven years ago there was a story. I was never named in the story. As far as I know, there was no investigation. But I did mention this to the party.”

Asked by TalkTV if he has always been faithful to his wife, he said: “Look, I mean, I have a fantastic marriage to my wife. And I’m really, you know, excited that we’ve built a fantastic family together. I don’t think it would be appropriate to talk about anything else.

“I have a loving relationship with my wife. We’ve been together for 22 years. We met originally in Bosnia after the war. And, you know, I’m thrilled to build a life and a family with her.”

The Conservative Party said on Tuesday that it is not investigating the claim.

Downing Street said Number 10 is a safe environment for women. It refused to be drawn on the individual case or whether there would be a Cabinet Office investigation into Mr Korski.

A Tory spokesman said: “The Conservative Party has an established code of conduct and formal processes where complaints can be made in confidence.

“The party considers all complaints made under the code of conduct but does not conduct investigations where the party would not be considered to have primary jurisdiction over another authority.”