The former prime minister's intervention came as Conservatives stepped up warnings over the potential outcome of the May 7 election, which opinion polls suggest will deliver the Scottish National Party as many as 50 seats and the balance of power in the House of Commons.
Sir John said Miliband's only route to 10 Downing Street involved a pact - whether in coalition or informal, and unacknowledged partnership - with the SNP, who he warned would subject the Labour leader to "a daily dose of political blackmail" pushing him "slowly but surely ... further to the left".
The SNP would use the position to demand policies favouring Scotland at the expense of the rest of Britain, driving a wedge between the nations of the UK with the hope of winning the 2016 election to the Scottish Parliament, the ex-PM argued. He also said it would pave the way for a second independence referendum.
Former Conservative British Prime Minister John Major makes a speech in Solihull, England, today in which he claims a Labour-SNP government would be "mayhem" for the UK
"They will ask for the impossible and create merry hell if it is denied," he warned. "The nightmare of a broken United Kingdom has not gone away. The separation debate is not over. The SNP is determined to prise apart the United Kingdom."
Arguing that it would be "perverse" for the electorate to remove Conservatives from office as recovery was taking hold, Sir John used a speech in the key Tory target seat of Solihull to urge voters - even the "disaffected, disengaged (and) downright fed-up" - to give David Cameron another term as prime minister.
Miliband accused Cameron of "demeaning himself and his office" by talking up the SNP's prospects in the hope that it would cost Labour votes and let him "crawl back" to power.
The Labour leader insisted there would be no coalition with the SNP and denied that Sturgeon's party would hold the whip hand on policy, telling BBC1's Breakfast: "A Labour government led by me, what happens in that Labour government will be decided by me, not by the SNP.
Scottish First Minister and Scottish National Party leader Nicola Sturgeon campaigns in Ayr, south west of Glasgow, today
"I think David Cameron is playing fast and loose with the United Kingdom. This is somebody who has given up hope of winning a majority. He is trying to boost the SNP.
"I think David Cameron is now threatening the integrity of the UK with the games he is playing. And I think Conservatives are now ashamed of what he is doing."
Sturgeon said Sir John's comments were "silly, over the top" and "an affront to democracy".
"My message to John Major is Scotland's voice deserves to be heard in whatever way the Scottish people choose, and voting SNP means Scotland's voice will be heard more loudly and strongly at Westminster than it has ever been heard before," she said.
Labour's Alistair Darling, who led the No campaign against Scottish independence, said the Tories were "flirting with English nationalism" in a "desperate" way which could lead to another period of divisive wrangling over Scotland's position.
There were signs of some unease among Tory ranks over the leadership's strategy, with former Cabinet minister Lord Forsyth telling the Guardian that the party's tactic of targeting a Labour-SNP link-up was "short-term and dangerous" and could ultimately damage the Union.
Sir John dismissed suggestions that he was stoking up division by demonising the SNP as "classic Labour spin", as did Cameron.
Speaking at an event in Leeds he said: "All I am doing is pointing out what is as plain as the nose on your face - which is, right now, Labour is facing a wipe-out in Scotland."
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Conservative Leader of the Commons William Hague told the BBC: "I think John Major is absolutely right to say what he is going to say in his speech today and to point to the danger of people who want to break up the United Kingdom in effect running the United Kingdom, if they hold the balance of power in Parliament.
"That's not talking up the Scottish National Party. Voters across the United Kingdom have to be aware of how serious this situation is, how serious this threat is, that it could actually happen."
Liberal Democrat leader Nick Clegg said Conservatives were "starting to argue amongst themselves because they are panicking".
Mr Clegg's predecessor as Liberal Democrat leader Lord (Paddy) Ashdown said Tory victory on May 7 would deliver a repeat of the destabilisation of Sir John's own government in the 1990s at the hands of eurosceptics within Tory ranks whom he branded "the bastards".