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Conservative MP Mark Garnier is to face an investigation into whether he broke ministerial rules after he admitted asking his secretary to buy sex toys.

The international trade minister also confirmed calling her "sugar tits," according to the Mail on Sunday, but he said it did not amount to harassment.

The Cabinet Office will look at whether the Ministerial Code of Conduct has been breached.

Mr Garnier did not respond to BBC requests for a comment.

It comes as the prime minister wrote to Commons Speaker John Bercow, calling for a new contractually-binding grievance procedure to be set up for all MPs and their staff.

Mrs May also asked Mr Bercow for his advice on how the culture at Westminster can be changed. Labour leader Jeremy Corbyn backed her call for reforms.

'Dinosaur behaviour'

Mr Garnier's former secretary, Caroline Edmondson, told the Mail on Sunday he had given her money to buy two vibrators at a Soho sex shop.

Ms Edmondson, who has since left to work for another MP, was quoted as saying that on another occasion in a bar, in front of witnesses, he told her: "You are going nowhere, sugar tits."

The Mail reported that Mr Garnier had admitted the claims, saying: "I'm not going to deny it, because I'm not going to be dishonest. I'm going to have to take it on the chin."

Mr Garnier conceded that his actions could look like "dinosaur behaviour" in the current climate, but added: "It absolutely does not constitute harassment."

The incidents date back to 2010 - before Mr Garnier was a government minister.

Speaking to the BBC's Andrew Marr on Sunday, Health Secretary Jeremy Hunt said recent newspaper reports about inappropriate behaviour by MPs and ministers were "totally unacceptable if true".

Asked about the working culture at Westminster, he said: "Things have got better in recent years but there is still some way to go.

"There are mums and dads who have daughters who are politics students hoping to get a job in Westminster, and they must be able to be confident that if they get that job, their daughter will not be subject to some of these behaviours that we have been seeing."

Media playback is unsupported on your device Media caption Diane Abbott: "Making sexual harassment a joke is one of the reasons it's not been dealt with"

'Undermining and demeaning'

Shadow Home Secretary Dianne Abbott told the Andrew Marr show the culture for women in Parliament had improved since she was elected in 1987, but said there was "still a long way to go".

She also criticised Conservative Environment Secretary Michael Gove, who was forced to apologise on Saturday after he likened being interviewed by BBC presenter John Humphrys to "going into Harvey Weinstein's bedroom".

"I heard it and I didn't think it was funny - particularly in Parliament, making sexual harassment a joke is one of the reasons it's not being dealt with," she said.

"You've got to realise that it's undermining and demeaning for women and undermines and demeans the institution."

Ms Abbott said Labour had set up a new process for dealing with complaints of sexual harassment, but she stressed that it was an issue for all parties to deal with.

Referring to Sheffield Hallam MP Jared O'Mara, who has been suspended by the Labour Party while it investigates misogynistic and homophobic comments attributed to him, she said: "That language and that tone is unacceptable".

Labour MP Liz Kendall told BBC Radio 5 live's Pienaar's Politics she knew of people in her own party who had not reported harassment "because they were urged not to". She backed the creation of a new independent reporting system.

Conservative MP Anna Soubry called for an urgent statement from Commons leader Andrea Leadsom on what can be done to ensure complaints are dealt with properly.

She told the Sunday Politics previous attempts by Conservative whips to set up a new grievance procedure had been frustrated by an inability to "get all the agreement that was necessary".

'Sexual chatter'

Meanwhile, former Welsh Secretary Stephen Crabb was reported by the Sunday Telegraph to have admitted sending "explicit" messages to a 19-year-old woman after a job interview at Westminster in 2013.

The married MP, who admitted meeting the woman "a few times," was quoted by the paper as saying he had been "foolish" but that there had been no sexual contact.

"I accept any kind of sexual chatter like this is totally wrong and I am sorry for my actions," the MP for Preseli Pembrokeshire said.

Mr Crabb resigned last year as work and pensions secretary following reports of a similar incident.

He did not respond to requests from the BBC for a comment.

Image copyright BBC Sport Image caption George Riley has reported on major sporting events for Radio 5 live

Elsewhere, the Sunday Times is reporting that BBC Radio 5 live sports broadcaster George Riley has been suspended, following claims that a number of women have complained about his behaviour.

Mr Riley has not commented and the BBC has not confirmed or denied the report.

A BBC spokesman said: "We can't comment on individuals but treat any allegations seriously and have processes in place for investigating them."