LONDON — A monitor at London’s City Hall has referred Prime Minister Boris Johnson of Britain to a police watchdog for a possible investigation of claims that he unduly favored an American entrepreneur while mayor of the city, intensifying a politically risky scandal as he faces a hostile Parliament and a looming Brexit deadline.

The official said the claims about Mr. Johnson’s ties to the entrepreneur, Jennifer Arcuri, who joined several of the mayor’s international trade missions and whose businesses were awarded tens of thousands of pounds in government money, were a “conduct matter” — essentially “an indication” that he may have committed “a criminal offense.”

The government’s response was fierce and dismissive: A cabinet minister from Mr. Johnson’s Conservative Party, Theresa Villiers, told the BBC on Saturday that it was “an obviously politicized complaint.”

Several British news outlets earlier quoted an unnamed government source as calling the referral “a nakedly political put-up job,” one done without warning to Mr. Johnson and without following due process.