In his letter of resignation, he said the party leadership had used any excuse "to allow their allies to attack Jews or engage with anti-Semites.
"My sad conclusion is that the Labour Party is very plainly institutionally anti-Semitic, and its leader and his circle are anti-Semitic having never once made the right judgment call about an issue reflecting deep prejudice," he wrote in the letter posted on Twitter by BBC Newsnight.
Former health minister Lord Darzi of Denham has also resigned the Labour whip.
The peer told BBC Two's Newsnight: "I confirm I am leaving the Labour Whip to sit as an independent.
"As an Armenian survivor of the Armenian genocide I have zero tolerance to anti-Semitism, Islamophobia or any other discrimination against religion or race.
"This decision has not been lightly taken."