A series of leaked email chains published by the BBC revealed purported efforts by Communications Director Seumas Milne and General Secretary Jennie Formby to protect party members accused of anti-Semitism.
Labour's deputy leader, Tom Watson, has stepped up his criticism of Jeremy Corbyn over antisemitism in the party by backing calls for automatic exclusion of members accused of anti-Jewish racism.
"I am shocked, chilled and appalled by what I've just seen on Panorama", he tweeted.
Speaking on BBC Radio Wales' Breakfast programme, he added: "The thing that was most rotten about the response to [the claims] was to try and rubbish their reputation, simply saying they were politically motivated and disaffected staff, as opposed to young men and women who've spoken out very bravely and honourably about what is clearly an bad situation".
Sir Keir Starmer said the party had to do "whatever is necessary" to win back critics who had deserted Labour over its handling of anti-Semitism claims.
He told BBC Radio 4's Today programme: "I think we have got to take decisive action".
But Watson said: "I deplore the statement that was made about those people last night; you couldn't fail to be saddened and moved by the testimony, particularly of the young members who'd had racist abuse in party meetings".
Gideon Falter, chief executive of Campaign Against Antisemitism, said the show was "heartbreaking".
A Welsh Labour MP has expressed sadness over claims some of Jeremy Corbyn's closest allies tried to interfere in disciplinary processes involving allegations of anti-Semitism.
"It was heartbreaking to watch the testimony of honourable lifelong Labour officials contemplating suicide and suffering breakdowns because of the actions of Mr Corbyn and his team", Mr Falter said. "Mr Corbyn's support for anti-Semites and his team's protection of anti-Semites demonstrate that Mr Corbyn himself is an anti-Semite who is unfit to hold any public office".
Senior Labour figures have been accused of interfering with the disciplinary process investigating claims of anti-Semitism in a BBC Panorama, claims repeated on the BBC's News at Ten and website.
"The Labour Party will fully investigate any complaints concerning the antisemitic incidents reported by party members in interviews in the programme". It showed the downplaying of serious allegations.
Former head of disputes Sam Matthews said he interpreted an email from Mr Milne as "not a helpful suggestion" but as "an instruction".
"After Jeremy became leader, he opened the floodgates and allowed people to join the Labour Party who never would have been allowed anywhere near it in the past", he told The Jewish Chronicle. "He is the biggest friend anti-Semites have had since the Second World War". A 2015 Panorama episode Ware produced on Corbyn made false claims and was widely denounced as a "hatchet job", while a 2005 program Ware produced about British Muslims was slammed as "McCarthyite" and "disgusting" - the latter by a former Panorama journalist.
"Our records show that after these officials left and after Jennie Formby became general secretary, the rate at which anti-Semitism cases have been dealt with, increased more than four-fold".
Labour described the programme as "seriously inaccurate" and "politically one-sided".
But a party spokesman said Labour was "taking decisive action to root out anti-Semitism from our movement and society" and said the documentary was "an overtly biased intervention by the BBC in party political controversy".
British Jewish groups have accused Labour of becoming institutionally anti-Semitic, and the issue has played a part in Labour's failure to take electoral advantage of the Conservative government's turmoil over Brexit.