The Conservatives have launched their own inquiry into whether politicians or officials gambled on the timing of the election, Rishi Sunak has said, as the prime minister denied that he had placed any bets himself. Sunak told reporters he was not aware of any further candidates being looked into and was not himself being investigated, saying he had never bet on a political event. The prime minister said he did not have further details of the investigation but Conservative campaign headquarters would “act on any relevant findings or information”. Four Tory candidates and officials are under investigation by the Gambling Commission, including Sunak’s top parliamentary aide, the candidate for Montgomeryshire and Glyndŵr, Craig Williams; its candidate in Bristol West, Laura Saunders; her husband and the party’s director of campaigning, Tony Lee; and the party’s chief data officer, Nick Mason, who has denied wrongdoing. An unnamed Metropolitan police officer who is part of Sunak’s close protection security team has also been arrested in connection with the inquiry into bets placed on a July election. Labour wrote to the head of the Gambling Commission on Sunday urging the watchdog to name those it had placed under investigation “in the public interest”, saying that “ongoing speculation … is casting a shadow over the election”. George Osborne, the former Conservative chancellor, told his Political Currency podcast earlier this month that about 40 people knew the date of the election in advance. Tobias Ellwood, the Tory former minister and candidate in Bournemouth East, said Sunak should be doing more to limit the damage, “given the scale of this, as we see now, and the potential for the story to continue to eclipse, to overshadow, the election. “I’m not sure anyone, including the prime minister, could have predicted the number of people involved when the story first broke. The public wants to see clearer, robust action.” Ellwood also said he thought the scandal would cost the Conservative party seats. “I have no doubt about it,” he said. Chris Heaton-Harris, the Northern Ireland secretary, who is standing down as an MP, was asked if he thought Sunak should have suspended the two candidates being investigated. He said they should remain until the investigation was complete. “I think what you’re trying to suggest is that someone is guilty until they’re proven innocent and that is not how this works,” he said. Keir Starmer rejected the suggestion that MPs should be banned outright from gambling after the scandal. Speaking at a school in Kettering, the Labour leader said: “I’m not sure we need to start changing the rules. The rules actually aren’t the problem here, there’s a problem with the politicians. The moment the election was called they didn’t say give me a microphone and let me make my case, they said let me head down to the bookies.”