Hanging over Mrs. May’s head are allegations against her deputy and longtime friend, Damian Green, the first secretary of state. Mrs. May called for an investigation into the case last week after a Conservative Party activist wrote that he had touched her knee and sent her suggestive text messages. Mr. Green has called the allegations by the activist, Kate Maltby, “untrue” and “deeply hurtful.”

Mrs. May has also ordered a Cabinet Office inquiry into Mark Garnier, her international trade minister, who has acknowledged asking his assistant to buy sex toys. In all, about a dozen members of Parliament, eight from the Conservative Party and four from Labour, are under investigation. One Tory, Charlie Elphicke, was suspended after “serious allegations” were referred to the police, the party has said. He has denied any wrongdoing.

“Britain’s political class feels pretty fragile right now,” said Tom McTague, the chief Britain correspondent for Politico and author of “Betting the House,” a new book on this year’s general election, in which the Conservative Party lost its overall majority, although it managed to cling to power.

“When something like this starts to get going, they just feel out of control,” he said. “The M.P.s don’t know where this is going. They don’t know how many allegations are going to come. They don’t know how to get on top of it.”

The episodes have unfolded against the peculiar structure of Britain’s Parliament: The 650 members of the House of Commons hire, employ and manage their staff personally, as if they were small-business owners.

Jess Phillips, 36, a Labour member of Parliament who worked with victims of sexual abuse before entering politics, recalled showing up on her first day in 2015 and asking a senior colleague where her employees should turn with workplace complaints.