Mr Warburton was suspended from the parliamentary party on Saturday evening after a series of allegations relating to sexual harassment and cocaine use.
The MP for Somerton and Frome, who is understood to be facing allegations from three women, while a photo has also emerged of the MP allegedly sitting alongside lines of cocaine. The picture of Warburton, published by the Sunday Times, is said to date from February. It is claimed it was taken at the home of a younger woman he met through politics.
Accusations from two other women have been handed to the new parliamentary harassment watchdog, the Independent Complaints and Grievance Scheme (ICGS).
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A spokesperson on behalf of the whips' office said: "David Warburton MP has had the Conservative party whip removed while the investigation is ongoing."
Replying to a question about the claims on Sky’s Sophy Ridge on Sunday programme, Mr Shapps said: “The party has, I think, withdrawn the whip, and put this under the investigation, which needs to go through its process. I don’t have any sort of further knowledge of it other than what I’ve read in the newspapers and what the party’s said.
“Obviously, any allegations like this need to be taken extremely carefully, but all the facts will need to be brought out as well. So until we get there I don’t think there’s much more I can helpfully add to it.”
Mr Warburton, 56, is reported to deny any wrongdoing.
The married father-of-two is alleged by the Sunday Times that he had described the price he paid for the cocaine as ‘quite good actually.
The woman involved claimed she had been drunk, but began to feel uncomfortable about being alone with the MP. She said that she retreated to her bedroom, but that he climbed into bed with her, naked.
She said she did not ask him to leave or push him away because she was fearful about how he might react. She said she gave repeated warnings that she did not want to have sex with him, but alleged that he ground his body against her and groped her breasts. The woman is said not to have made a complaint to the police, saying she wanted to forget the incident.
The MP has previously condemned the exploitation of young people involved in the drugs trade. The ICGS was set up to tackle misconduct by MPs, peers and staff after complaints about misconduct. It has now been handed allegations that Warburton behaved inappropriately. Warburton's Twitter account appeared to have been deleted yesterday. The Observer approached Warburton for comment last night. When contacted by the Sunday Telegraph, he said: "I have enormous amounts of defence, but the way things work means that doesn't come out first. I can't comment any further."
Warburton employs his wife, Harriet, in his private office. He was first elected to parliament in 2015, with a large majority of more than 20,000 votes.
If he is forced to stand down, the Lib Dems would be hopeful of taking his seat after their shock wins in former Tory seats Chesham and Amersham and North Shropshire last year.