Labour’s general election candidate for Kensington and Chelsea has said she will report her Liberal Democrat rival to the police, alleging he made a false statement implying she had a role, as a local councillor, in discussing the flammable cladding used on Grenfell Tower.

Emma Dent Coad, who became MP for the west London constituency in 2017 and is an ally of Jeremy Corbyn, said Sam Gyimah’s claims were “shameful” and accused him of whipping up false rumours that could lead to her being the target of violence.

She said she had given him several days to withdraw his comments and a complaint to the Metropolitan police under the Representation of the People Act would be issued later on Sunday.

Dent Coad said: “If this is a political game, shame on him. We’ve sent rebuttals with all the links and all the evidence is there. Even if I had been on those committees, there is no way that a backbench opposition councillor would have made those decisions. But I wasn’t on those committees at that time and I can prove it.

“That’s really, really dangerous talk. I’ve given him plenty of opportunity to withdraw it and if he’d said he’d made a mistake, I would have said let’s move on with this election. But he hasn’t withdrawn it.

“He should be thinking about what he’s doing … he’s putting not only me but my volunteers in danger.”

Gyimah, a former Tory minister who defected to the Lib Dems over Brexit, made the contested comments to City AM last week.

Asked if he felt the Tory government’s austerity measures had contributed, he said: “Many things went wrong and, by the way, Emma Dent Coad was on the council and was part of all the discussions that went on in terms of cladding.

“If we are going to get into the blame game, it’s a very complicated one. To just say ‘of course it’s the Tory government’ – well, the council is responsible, and there were Labour councillors there who could have stopped some of the decisions and didn’t.”

Dent Coad has written a rebuttal to the accusations, first made by her Tory rival Victoria Borwick in the days after the fire in 2017.

The Labour candidate said she joined the board of the tenant management organisation for Grenfell in June 2008 and left in October 2012, and it was only after this point that planning applications for the refurbishment of the tower and any discussions about its substance happened. She also denies having scrutinised any decisions about the Grenfell refurbishment while a member of council housing committees.

She said: “To be clear, I was on the board when the principle of refurbishing Grenfell Tower was discussed, but I was nowhere near the decision-making process for the detailed specifications for refurbishing Grenfell, which started when I left. Board members agreed the contract but do not specify cladding or indeed any other technical details. Neither should they.”

Dent Coad said one of her volunteers was assaulted in the street for defending her when her Tory rival had first made the claim that she bore “collective responsibility” for the Grenfell refurbishment.

Under the Representation of the People Act, it is illegal during an election period for any person to “publish any false statement of fact in relation to the candidate’s personal character or conduct, unless he or she can show that he had reasonable grounds for believing that statement to be true”.

A Lib Dem spokeswoman said the party had received no contact from police.