The former Prime Minister made the explosive intervention as he warned “the very structure” of British politics is now threatened by leaving the EU.
Sir John said “you may be driven to a national government” – which he said would have to involve inviting members of the opposition to join the Cabinet for the first time since the 1940s.
“I don’t like this idea, I don’t think it’s ideal,” Sir John told the BBC’s Andrew Marr Show.
“But I do think in the interest of the nation, in the interests of decisions being taken, in the interests of ending the chaos we have now and that could continue, we must have a government that has a working majority.
“And that is the only reason for a time-limited unity government.”
Sir John said he believed a national unity government was not imminent, but it was also “very unlikely” a general election now would produce a clear majority.
He told the BBC: “If we have a general election in the autumn, which I think is possible not certain, and we don’t get a government with a clear majority then I think it would be in the national interest to have a cross-party government.
“So that we can take decisions without the chaos that we’re seeing in Parliament at the moment, where every possible alternative is rejected.”
Asked for his advice to Mrs May about whether or not she should call an election this week, Sir John replied: “Don’t. I mean don’t for a whole range of reasons.
“The Prime Minister is blocked in on every side, I utterly can empathise with her frustration but I think a general election will solve nothing at this moment.”
Sir John said “of course” the situation now doesn’t compare with the unity government of the war years.
But he warned Britain risks “constitutional chaos” stretching for “a very long time ahead”. He added: “If you consider what is at stake at the moment.
“The living standards of the British nation.
“The worldwide reputation of Britain, which has not done well during this argument about Brexit.
“The unity of the UK and whether we lose Scotland and Northern Ireland.
“And the very structure of our politics, which is now threatened.
“If that doesn’t collectively constitute and constitutional and political crisis, then I cannot imagine what does.”
The Prime Minister’s aides are said to be weighing up whether to go to the country after she warned the process was “reaching its limits” in the Commons.
According to multiple reports today, some No10 officials think an election could unclog Parliament after MPs blocked the Brexit deal a third time on Friday.
But others, including Mrs May’s Chief Whip Julian Smith and chief of staff Gavin Barwell, are said to bitterly against the idea.
And one Tory MP even suggested he could vote against any motion to hold an election, which would have to be put to the House of Commons.
He told the Sunday Telegraph: “We would be annihilated. How many of us would vote for that?”
Conservatives have collapsed into infighting since Friday, when Theresa May’s Brexit deal suffered a third defeat by a 58 majority – including 34 Tory rebels.
The PM could be forced into accepting a softer Brexit with a customs union as MPs stage “indicative votes” on the way forward tomorrow night.
But 170 Tory MPs backed a letter against a customs union, with some warning it would “break the party” in the worst split since the Corn Laws 173 years ago.
So Mrs May is expected to put her thrice-defeated Withdrawal Agreement before MPs for a FOURTH time this week.
The UK needs a deal by April 12 otherwise it must either cancel Brexit; crash out with no deal; or seek a “long extension”.
Tory Vice Chair James Cleverly today said “were not planning for a general election” and called it “belly button gazing” but did not rule one out.