Writing in the Sunday Telegraph the former prime minister attacked Brexit campaigners' pursuit of independence as "sheer folly" and "verging on the reckless".
Being part of the European Union not only benefits the UK in terms of prosperity and security but is also essential for maintaining stability within the Union and its relevance on the world stage, he said.
"I cannot believe that any sensible Briton wishes to divide Europe, and thus divide the West," the Press Association reported the Tory grandee as saying, as he branded attempts to tear up Britain's existing bespoke deal as "perverse".
Sir John accused some in the Leave camp of ignoring and even obscuring "facts" that did not sit well with their objective, including statements from European leaders that there will be no trade deals without free movement and an invoice for access to the single market.
His intervention comes after Iain Duncan Smith, one of the leading figures in Vote Leave, accused the Government of issuing a "dodgy dossier" to support its campaign to remain in the EU.
Brexit campaigners have claimed that the remaining 27 EU members would be eager to arrange new trade deals with the UK in negotiations where Britain could have the upper hand.
Sir John wrote: "This is self-deception to the point of delusion. Their argument is that the EU needs the UK market more than we need theirs, on the basis that - overall - the EU exports more to the UK than we export to them.
"This is, at best, disingenuous. More bluntly, it is fantasy."
He said Britain's influence on Europe would only be maintained within the bloc, adding that any trade from the outside would still be on Brussels' terms.
The reality may be that Britain finds itself on the fringe of a Europe that is either consolidated against it or fractured beyond repair, he warned.
"Resentment will be deep. The broken relationship is more likely to be poisonous than harmonious. The UK will have chosen to leave and, by so doing, will have gravely weakened the whole of the EU."
The Leave campaign has regularly accused the Government of deploying "Project Fear" to dissuade voters from opting out of the EU – a slogan dismissed by Sir John as "flippant".
Brexit campaigners have also accused the Government of attempting to silence prominent Euroceptics. Downing Street made strong denials when it was accused of a stitch-up over the resignation of John Longworth, former director-general at the British Chambers of Commerce.
Sir John highlighted how a number of individuals, bodies and organisations, including the G20, military leaders, the governor of the Bank of England Mark Carney, and figures from the sciences, have in recent weeks spoken of the benefits of remaining in the EU.
"Are they really all guilty of 'interfering', 'scaremongering', or being part of one enormous plot being orchestrated by No 10? Such a notion is absurd," he wrote.
As a politician whose career began in the 1970s, he argued that Britain had joined the bloc as "the sick man of Europe", whereas the UK is now one of its best performing economies and a major factor in its influence on the world stage.