But the acclaimed politics professor says the Labour leader could still make it to No.10, with a Corbyn-led minority government one of the two possible outcomes from the general election.
He says the election campaign is an "unpopularity contest" with the outcome deciding whether the UK will soon leave the EU under the Conservatives, or hold a second referendum on Brexit under a loose gathering of centre-left parties.
With the Tories averaging a lead of around 10 points in the polls, Labour's chances of winning a majority of seats in Parliament look slim.
Sir John, a professor at the University of Strathclyde, told reporters: "The chances of the Labour party winning a majority are frankly as close to zero as one can safely say it to be given they look utterly incapable of regaining anything in Scotland." He added: "With a 10-point lead, the Tories are likely to win an overall majority."
Edinburgh University's Ailsa Henderson warns the party could be undermined by the failure to project a clear message on Brexit, unlike the pro-Leave Tories and pro-Remain Lib Dems and SNP.
She compares Labour's Brexit policy to its stance on Scottish independence which has led to a slump in the polls north of the border, and says: "We know the consequence of having an on-the-fence policy and it is utterly disastrous."
One reason for Labour's weakness is the party's collapse in Scotland, which started after the independence referendum five years ago. Professor Henderson says: "In Scotland, no one is moving to Labour - no-one."
The political situation in the country has been transformed by the double effect of the independence and Brexit referendums, forming four voting blocs: Yes/Remain, Yes/Leave, No/Remain and No/Leave.
"Boris you might want to regard as like a Ming vase," Sir John says. "He's potentially a really valuable asset - you just want to make sure he doesn't fall on the floor."
He warns the Prime Minister is remarkably unpopular for an incoming national leader, adding: "That's essentially, of course, basically because Boris is loved by Brexiteers and he is hated by Remainers, so he is Marmite.
"The thing you have to bear in mind now is that the Boris Johnson we have now is not the Boris Johnson who was mayor of London, who was able to reach across the political divide in the capital.
"The Boris Johnson we have now is very firmly regarded as the person who is responsible for Brexit and is now trying to deliver Brexit and Remain voters regard him accordingly."
Winning in Wales
Labour have been the largest party in Wales at every general election since 1918, Professor Roger Awan-Scully of Cardiff University explains. But polls show the Conservatives running a strong second this time around.
At least 10 of Labour's 28 seats are looking shaky, with the Tories the main challenger in each of them. Five seats in north-east Wales are particularly vulnerable - including Wrexham, likely to be the first Welsh constituency to declare its result on election night.
"If the Conservatives have not gained Wrexham then I think Boris Johnson is likely to be an ex-Prime Minister very soon," Professor Awan-Scully says.
Nothing has changed
"As a certain person would say, nothing has changed - not very much," Sir John says, channelling his inner Theresa May.
The polls have remained remarkably stable since the election was called, with the Tories and Labour both rising slightly at the expense of the larger parties.
Sir John - who will co-ordinate the nationwide exit poll on election night - predicts the Brexit Party's partial withdrawal will help the Conservatives. All of which leaves Mr Corbyn a mountain to climb if he wants to get into power.