Home secretary Mr Cleverly said he would not defend any Tories found to have placed bets, but that it was a matter for the Gambling Commission to investigate.
Senior individuals are putting increasing pressure on Rishi Sunak to step in and address the Tory general election betting crisis.
The prime minister has been requested to convene a Cabinet Office probe into the matter and to suspend from the party all those who are under investigation right away.
Regarding the situation, party head Richard Holden, who is in charge of the Conservative general election campaign, has said almost little.
A former Tory minister and the deputy leader of the Liberal Democrats are among those who joined the growing call for the people involved to be suspended.
Labour’s national campaign coordinator Pat McFadden wrote to the Gambling Commission asking the watchdog to release the names of all those being investigated.
As the deepening crisis threatened to derail the Tory election campaign for yet another week:
Amid the growing fallout, former justice secretary Sir Robert Buckland told LBC he was dismayed by the scandal. “Whatever the motivation of these people ... is this really what we expect? I think not,” he said.
Asked whether he thought the PM should suspend those involved, he said: “I do.”
And former chancellor Kwasi Kwarteng told GB News: “It’s childish and incredibly stupid. How did they think they wouldn’t be caught?” He pointed the finger at Mr Sunak, saying he is in charge so is “ultimately responsible”.
He went on: “Sometimes it might be unfair, maybe he didn’t know what was going on, but as the leader of an organisation, your character, your job is to impose some sort of discipline on the institution, and if things go wrong – I know it’s an old-fashioned view, and people don’t really subscribe to it any more, but ultimately I think the leader bears responsibility for what’s going on.”
After a day of silence from the prime minister, Lib Dem deputy leader Daisy Cooper told The Independent: “Rishi Sunak must personally intervene to order a Cabinet Office inquiry and suspend all those under investigation by the Gambling Commission.
“People are sick and tired of this sleaze. Day by day, hour by hour, the Conservative government mire themselves in more of it.”
In his damning letter to the Gambling Commission, Mr McFadden said: “With postal ballots already being sent out, many millions of people will be casting their vote this week. They deserve to have all relevant facts about this scandal at their disposal when doing so.
“I believe it is in the public interest that the Gambling Commission makes public the names of other figures you are investigating relating to this matter. There will be particular interest in whether any government ministers bet on the date of the election before it was called.”
The Independent has revealed that an unnamed cabinet minister is believed to be among several figures being investigated, with numerous senior Tories ruling themselves out including Grant Shapps, Penny Mordaunt, James Cleverly, Mark Harper and Mr Gove.
Over the weekend, the Conservative Party’s chief data officer Nick Mason became the latest figure to be placed under investigation by the Gambling Commission.
He is the fourth named figure close to the party leadership to come under investigation by the gambling watchdog for allegedly betting on the timing of the election before the date had been announced.
The latest allegations were published by The Sunday Times, which claimed that dozens of bets had been placed by Mr Mason with potential winnings worth thousands of pounds.
Mr Gove said: “The perception that we operate outside the rules that we set for others – that was damaging at the time of Partygate and is damaging here.
“If you’re in a privileged position, [close] to the prime minister, at the heart of a political operation, and you use inside information to make additional money for yourself, that’s just not acceptable. So if these allegations are true, it’s very difficult to defend.”
Home secretary Mr Cleverly said he would not defend any Tories found to have placed bets, but that it was a matter for the Gambling Commission to investigate.
He said: “My understanding is that it is a small number of individuals” involved, adding: “There is an investigation by the Gambling Commission, and we have been told very, very clearly that we are not to discuss the investigations.”
Several reports suggested that the commission was investigating “many more” individuals and had widened its inquiry to include potential bets by family and friends of those connected to the party.
An industry source told The Independent that the Gambling Commission had asked for details of all the bets made on a July election after 1 May, and that it is now “combing through the data and picking off people from that”.
The revelations are a fresh blow to Rishi Sunak’s hopes of getting the Tory election campaign on track, after three other Conservative figures were caught up in the scandal.
Craig Williams, Mr Sunak’s parliamentary private secretary, who is standing in Montgomeryshire, was the first Tory candidate to be publicly linked to the betting scandal.
Laura Saunders, who has worked for the Tories since 2015 and is standing in Bristol North West, and her husband Tony Lee, director of campaigning, are both being investigated.
Shadow education secretary Ms Phillipson described “genuine disgust” among voters over the general election betting.
She told the BBC’s Sunday with Laura Kuenssberg: “People across the country will place bets, but I think there is genuine disgust amongst so many voters that what we’re seeing here is pretty shocking behaviour.
“Rishi Sunak promised us that his government would be different; he hasn’t acted against candidates concerned, he should suspend them, and – as Michael Gove has said – this just reminds people of the worst excesses of the Conservatives over the last 14 years.”