Despite criticism, she doubled down, saying: “I’ve done anti-racist politics all my life…why am I any more or less a legitimate voice to offer an opinion?”
Sir Simon tweeted that he was “horrified” by the BBC’s decision and that “someone should have had editorial second thought! Really appalling.”
The Board of Deputies called it "insensitive and provocative".
Board President Marie van der Zyl said: “We would ask the BBC to explain why someone who defended the desecration of a memorial to the Warsaw Ghetto Uprising has been invited to speak on a programme about the rise of the Nazis.
"Given the outrage her comments have caused, the invitation by the programme makers seems both insensitive and provocative.”
Jewish historian Simon Sebag Montefiore called it "a pretty unfortunate choice of 'expert'" that "undermined an otherwise admirable history programme".
Other Jewish figures condemned the inclusion of Ms Sarkar,who describes herself as a Communist and is a frequent commentator on TV defending Jeremy Corbyn's Labour Party.
Countdown presenter Rachel Riley said including Ms Sarkar on the programme was “upsetting and downright insulting”, while actress Tracy Ann Oberman tweeted “as someone who lost family during The Rise of The Nazis" to ask Patrick Holland, BBC Two’s channel editor, why Ms Sarkar had been used as part of the documentary.
“I am deeply disturbed that of all knowledgeable experts/historians, you use…a woman who endorsed the spray painting of the remaining Warsaw Ghetto wall - an open grave for our families", she wrote.
Ms Oberman went on to say she was “sure BBC Two didn’t mean to cause offence…but it has and it makes a mockery of the subject matter.”
A number of British Jews confirmed that they had already complained to the BBC.
Responding on Tuesday morning to the outrage, Ms Sarkar tweeted: “Apparently a lot of the usual suspects are very angry with BBC 2 for asking me to talk on their Rise of the Nazis series”, saying she had been asked to talk about German Communists and Stalinism.
“I don’t see why my support for Boycotts, Divestment and Sanctions against the Israeli occupation of the West Bank should disqualify me from talking about the Communist party of Germany”, she said.
She added she “obviously reject(s) wholeheartedly claims of antisemitism” and said she had received racist abuse over appearing on the programme.
The BBC defended featuring Ms Sarkar. A spokesperson said: "As well as featuring interviews with some of the world's leading experts on pre-war Germany, this series asks recognised contemporary figures from different professional fields, amongst them historians and journalists, to examine in detail the motives and experiences of individual historical figures from this period.
"Ash Sarkar is one of a number of current public figures who feature, alongside representatives from military and legal backgrounds.
"She appears in this film in her role as a self-declared communist and lecturer in political theory and her contribution to the series is solely to illuminate the context and perspective of Ernst Thälmann, the leader of the Communist Party of Germany (KPD) from 1925 to 1933, who died in a concentration camp in 1944."
