A minister has said he bet on the Conservatives winning the election, but said gambling on the result in his constituency would be “wrong”.

Kevin Hollinrake, a business minister, told broadcasters he had bet on his party to win a parliamentary majority “some months ago”. Asked whether he had bet on a Tory victory, Hollinrake told Times Radio: “Yes, I did. Not my seat, I think that would be wrong.”

Hollinrake is standing for re-election in Thirsk and Malton. “We should have a proper debate about and decide whether it’s right or wrong that people have a bet on things they are involved in,” he said.

Hollinrake said he thought the odds were 9:1 when he placed his bet. “You may think that’s foolhardy,” he joked on LBC. “Victory is always possible if you don’t stop fighting.”

Asked whether there were more Conservatives who could have broken the rules, Hollinrake said: “Anybody who has broken the rules will be booted out of the Conservative party … the prime minister believes in process, as I do.”

The election campaign has been overshadowed by a gambling scandal since the Guardian revealed that Craig Williams, a Tory candidate who was Rishi Sunak’s closest parliamentary aide, bet on a July election three days before it was announced.

Williams is under investigation by the Gambling Commission. It is a potential offence to use insider information to gain unfair advantage when placing a bet.

Since then it has emerged that another Tory candidate, two senior party officials, several police officers and a Tory member of the Welsh parliament are also being investigated by the gambling watchdog for betting on the election date. A Labour candidate is also being investigated after he bet against himself in his constituency.

The Sun reported on Wednesday that the Tory candidate Philip Davies had also bet against himself at the election, placing £8,000 on losing his marginal seat of Shipley.

There is no suggestion that the veteran Tory, who is married to the cabinet minister Esther McVey, has broken the law. He did not dispute the sum but told the Sun it was “nobody’s business”.

Sunak and Keir Starmer clashed over the scandal at a BBC head-to-head debate last night. Starmer accused the prime minister of having been “bullied” into action.

The Labour leader said he had suspended his candidate, Kevin Craig, “within minutes” and compared his actions with those of Sunak, who took days to make the decision.

Starmer said: “I think that in the last 14 years politics has become too much about self-entitlement and MPs thinking about what they could get for themselves.

“The instinct of these people to think the first thing they should do is try to make money, that was the wrong instinct, and we have to change that.”

Sunak responded that he was “furious” about the allegations and had launched an internal Conservative party inquiry.