Three Labour peers have resigned over the party’s handling of antisemitism complaints, with the former general secretary David Triesman arguing the party was “plainly institutionally antisemitic”.

Lord Triesman, who is Jewish and an ex-chairman of the Football Association, said he was resigning the whip in the House of Lords.

Ara Darzi, a former health minister, and Leslie Turnberg, a former president of the Royal College of Physicians, also told Angela Smith, the party’s leader in the Lords, that they were leaving the Labour benches.

Another prominent Jewish politician, Luciana Berger, resigned in February in protest at the party’s handling of complaints of antisemitism, along with six other Labour MPs.

In his letter of resignation, Triesman wrote: “We may one day be the party of anti-racism once again but it certainly isn’t today. My sad conclusion is that the Labour party is very plainly institutionally antisemitic, and its leader and his circle are antisemitic having never once made the right judgment call about an issue reflecting deep prejudice. The number of examples is shocking.”

He said the Labour party was “no longer a safe political environment” for Jewish people or others who opposed antisemitism.

“It it time to recognise the reality. I always said it was worth hanging on to fight so long as there was a prospect of winning. I now don’t believe with this leadership there is,” he said.

Triesman has in the past been targeted by antisemitic attacks on his home by Combat 18, a banned neo-Nazi terrorist group. It orchestrated a 14-month campaign against him in 2004, breaking his windows and daubing his walls with swastikas in 12 separate attacks.

Lord Darzi told the BBC’s Newsnight: “As an Armenian descendant of a survivor of the Armenian genocide I have zero tolerance to antisemitism, Islamophobia or any other discrimination against religion or race.”

Responding to the peers, a Labour spokeswoman said the party “completely rejects these false and offensive claims”.

She said: “The Labour party at all levels is implacably opposed to antisemitism and is determined to root out this social cancer from our movement and society.

“Labour is taking decisive action against antisemitism, doubling the number of staff dedicated to dealing with complaints and cases. And since Jennie Formby became general secretary, the rate at which antisemitism cases have been dealt with has increased four-fold.

“Our records show that antisemitism cases that have gone through the stages of our disciplinary procedures since September 2015 account for about 0.06% of the party’s membership. This represents a tiny minority, but one antisemite is one too many, and we will continue to act against this repugnant form of racism.”

It is understood the party particularly disputes the claim that “antisemites are shielded” and argues that it should not be reported without evidence and without the party having the opportunity to respond to specific allegations.

Labour has defended its handling of complaints, with Jeremy Corbyn promising members he would speed up disciplinary cases to drive antisemitism out of the party and stressing that it has always fought racism in all its forms.

However, there has been an outcry over the case of Chris Williamson, the Derby North MP, who was suspended for saying Labour had been “too apologetic” about complaints of antisemitism, and then reinstated with a reprimand.

Williamson was suspended again after a backlash within Labour and a national executive committee meeting decided on Tuesday that a new disputes panel must be formed to examine the decision once more, potentially referring it for further investigation.

• This article was amended on 10 July 2019 to correct a misrendering of a quote from Lord Darzi.