Scotland Yard will investigate any suspicious bets that could represent a misconduct in public office offence, while the Gambling Commission will continue to look at whether betting rules were broken.
The prime minister repeatedly refused to say whether he told Williams, his closest parliamentary aide, about the date of the election, wrongly claiming he could prejudice the watchdog's inquiry.
So far five Conservatives are known to have been caught up in the Gambling Commission inquiry since the Guardian first revealed two weeks ago that Williams had placed a £100 bet with Ladbrokes three days before Sunak announced the date.
The Tories have withdrawn the party's support for Williams' bid to be returned as the MP for the Montgomeryshire and Glyndwr seat, after he admitted having a "flutter" on the election date.
During a campaign visit in Derbyshire, Sunak was repeatedly asked whether he had confided in Williams before his surprise announcement of a summer election.
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