He has previously spoken of how he felt he had truly been accepted by the Jewish community when his husband began to receive invitations to events at synagogues.
But Mr Freer told the Pink News website that supporters had been canvassed by Labour activists who had told them he was gay.
“Some of my Orthodox Jewish councillors were out knocking on doors and three residents also mentioned that they had had Labour round, and it had been brought up again, and they could no longer support me because I was gay,” Mr Freer told the website.
“If it’s true, it’s appalling. It’s a sign of desperation.”
Ms Sackman said: "Homophobia has no place in our society or in an election. I publicly support equal marriage and LGBT rights.
"If Mike Freer has any evidence supporting the statement he made to Pink News he should refer it to the police. That is the proper way to deal with this."
Ms Sackman said there were around 300 canvassers working on her campaign and said Mr Freer's claims were "odd".
The battle for Finchley and Golders Green is predicted to be one of the tightest in the country. Mr Freer has a majority of more than 5,800, but recent polling has suggested Ms Sackman is narrowly ahead.
