Video report by ITV News Political Editor Robert Peston
Sir John Major has called on Theresa May to inject "a little more charm and a lot less cheap rhetoric" to sweeten the "already sour" atmosphere ahead of Brexit negotiations.
The former Tory prime minister also hit out at the "unreal and over-optimistic" promises being made to the British public before talks begin in late March.
He warned the country's most vulnerable people will be hardest hit by the impact of leaving the European Union in a key speech in which he hit back at criticism being levelled at dissenting Remain voices.
ITV News Political Editor Robert Peston said Sir John had issued a "savage attack" on Tory Brexiteers as he condemned the Brexit vote as a "historic mistake".
Sir John said he had watched with "growing concern" at the Brexit vision projected by Mrs May's government.
"Obstacles are brushed aside as of no consequence, whilst opportunities are inflated beyond any reasonable expectation of delivery," he said in a speech at Chatham House in London.
He warned Mrs May and her Brexit negotiation team that talks require "statesmanship of a high order".
He said there was a "real risk" the exit deal will fall "well below the hopes and expectations" that have been raised, with "little chance ... to match the advantages of the single market".
Sir John said Mrs May's negotiation team had created an "already sour" atmosphere towards Europe's negotiators.
"In my own experience, the most successful results are obtained when talks are conducted with goodwill," he said, adding: "It is much easier to reach agreement with a friend than a quarrelsome neighbour."
Sir John's latest speech comes after fellow-former PM Tony Blair was widely attacked for his latest intervention in the post-referendum debate.
But Sir John defended the right of Remain voters to question, disagree or express dissent in Britain's direction as he called on pro-Leave voters to "stop" attacks he said were demeaning and intolerant.
"It's not 'arrogant' or 'brazen' or 'elitist', or remotely 'delusional' to express concern about our future after Brexit," he said.
Sir John also said Brexit had "energised" anti-EU, anti-immigrant nationalism in other European countries but condemned the "populism" as a "mixture of bigotry, prejudice and intolerance".
"It scapegoats minorities. It is a poison in any political system - destroying civility and decency and understanding," he said.
Sir John said Mrs May forging of a close-knit relationship with Donald Trump's administration was a threat to Britain.
He said Britain risks becoming more dependent on the United States led by a president who is "less predictable, less reliable and less attuned" to Britain's ways than his predecessors.
Sir John said the public should also be more aware that the ideological trade positions being demanded by some Leave supporters posed a genuine threat to the NHS and state pension and welfare systems.
"We cannot move to a radical enterprise economy without moving away from a welfare state," he said as he warned against the UK adopting World Trade Organisation rules.
"There is a choice to be made, a price to be paid," he said.