The Conservative party is facing new questions over the role Rishi Sunak’s closest parliamentary aide played in pre-election discussions before he placed a bet on the poll date days before it was announced.

Labour has written to Richard Holden, the Tory party chair, demanding more answers on the scandal that has further marred the party’s bruised election campaign.

The Guardian revealed on Wednesday that Craig Williams placed a £100 bet with Ladbrokes on a July poll. Williams, the prime minister’s parliamentary private secretary who is standing for re-election in Montgomeryshire and Glyndŵr, placed the bet on 19 May in his local constituency.

The Gambling Commission launched an inquiry after the bet was referred to them by the bookmaker.

Anneliese Dodds, chair of the Labour party, has urged the Tories to remove the whip from Williams, if he were to win his seat and the inquiry finds he had used privileged information to place the bet.

She says “even the suggestion of impropriety must be investigated fully by the Conservative party”, or risk Rishi Sunak going back on his promise of “professionalism, integrity and accountability”.

She added: “The suggestion that Craig Williams could have been using privileged information to place this bet is an extremely serious allegation. If this is true, then he has no place on the Conservative benches, if he is to win his seat. Even the suggestion of this – which could amount to cheating, a criminal offence under the Gambling Act – is deeply corrosive to trust in politics.

“With this in mind I must ask you: what was Craig Williams’ role in discussions around the election date, when could Craig Williams have had a reasonable idea that a July election was a realistic possibility and when did the Conservative party know about this bet and the investigation by the Gambling Commission?”

Williams has apologised, saying he “clearly made a huge error of judgment” and that he would comply with the commission’s inquiry.

The prime minister on Thursday refused to be drawn on whether he would disown Williams as a candidate. “It is very disappointing,” Sunak said.

“Craig Williams has said that it’s a huge error of judgment. Now there is an independent inquiry which is confidential and it’s important that that is allowed to continue. It’s not appropriate to say anything while that’s ongoing.”

It understood the watchdog wrote to all licensed bookmakers this week requesting information on anyone who stood to gain more than £199 by betting on a July election in the UK.

Holden received the letter from Labour as he still faces questions and anger over his last-minute selection. He was selected for the safe seat Basildon and Billericay, Essex, 300 miles from his former constituency, after being the only candidate on the list.