Lord Blunkett, who was an MP for 28 years and now sits as a Labour peer in the upper chamber, said the likelihood of Jeremy Corbyn winning a majority was "extraordinarily slim".
But he urged moderates within the party to "stay and fight" to ensure the "voice of reason" prevailed, following deputy leader Tom Watson's decision to stand down.
The former Cabinet minister and party chairman's comments came after a bruising week for the party which has seen two of its former MPs urge voters to back the Tories instead.
Ian Austin and John Woodcock said they would be supporting the Conservatives as they did not believe Mr Corbyn was fit to be in Number 10.
And on Friday, Dame Margaret Hodge - one of the most prominent Jewish figures in Labour - declined to endorse the Opposition leader as prime minister.
Writing in the Telegraph, Lord Blunkett said: "The behaviour of the hard-Left within the Labour Party - the anti-Semitism, the thuggery, the irrational views on security and international issues, and the lack of realisation that you have to embrace a big tent of people in order to win - certainly makes me despair.
"But it also makes the likelihood of an all-out Labour majority in this general election extraordinarily slim. The political landscape right now is completely different to what the hard-Left would have you believe.
"We are in a 1983 situation here, not a 2017 one - with not only the Lib Dems and the Greens, but the Brexit Party, the Tories and the SNP all seriously vying for traditional Labour votes."
The 1983 election saw Margaret Thatcher's Conservative Party secure a sizeable majority after votes for the opposition were split between Labour and the Liberal/SDP Alliance.
His intervention comes after another Labour candidate stepped down after allegedly making an anti-Semitic remark.
Gideon Bull, the prospective parliamentary candidate for Clacton, apologised after a Jewish councillor complained about a reference he made to "Shylock" - the Jewish moneylender in Shakespeare's The Merchant Of Venice.
Meanwhile, Boris Johnson came under fire after he suggested his Brexit agreement was a "great deal" for Northern Ireland as it would retain access to the EU single market and maintain freedom of movement.
Labour will attempt to get its campaign back on track as Jeremy Corbyn visits Leeds to announce proposals to provide 30 hours per week of free care to all children aged between two and four.
Mr Corbyn and shadow education secretary Angela Rayner will announce the proposals to provide 30 hours' publicly-funded childcare every week for all pre-school children over the age of two.
It comes on top of a £1 billion investment programme to reverse Conservative cuts in order to open 1,000 extra Sure Start centres in England to support young families.
According to party-commissioned analysis from the independent House of Commons Library, Labour's election childcare offer has the potential to save the average parent of a two-year-old more than £5,000 every year.
The Conservatives, meanwhile, will pledge to create 50 million more appointments in GP surgeries every year if the party wins a majority at the December poll.
Health Secretary Matt Hancock said the additional appointments - to be in place by 2024-25 - would be made possible by thousands more doctors, nurses, physiotherapists and pharmacists.
Liberal Democrat leader Jo Swinson will also hit the campaign trail on Saturday as she sets out her party's vision to stop Brexit and "build a brighter future" at a rally in London.
The party will announce plans to introduce free childcare for children aged between nine months and 24 months where their parents are in work.
It has also pledged to provide free, high-quality childcare for every child aged two to four for 35 hours per week for 48 weeks a year.
Elsewhere, the Conservatives have come under fire as the Guardian reported the number of NHS patients having surgery in private hospitals has nearly trebled since 2010.
The paper said the NHS paid for 214,967 people in England to have an operation in a private hospital in 2009-10, but that the figure rose to 613,833 last year.