David Cameron promised further devolution for Scotland if it voted against independence, and rejected the idea of a currency union with an independent state, as he launched his personal campaign to save the United Kingdom.

In a dramatic intervention the UK prime minister claimed there are just “seven months to save the most extraordinary country in history”, warning that the country would be “deeply diminished” if Scotland votes to secede in this year’s independence referendum.

The prime minister on Friday promised Scots further devolution of powers from London if they vote “no” in September, a pledge the pro-independence Scottish National party has repeatedly called into question.

Mr Cameron also insisted it would be “extremely difficult” to form a currency union between an independent Scotland and the rest of the UK, on the same day an economic study said that any currency union would be liable to break apart, particularly due to Edinburgh’s public finance challenges.

The prime minister’s currency warning chimes with similar statements from the chancellor and the governor of the Bank of England, as the British government ramps up the pro-union rhetoric and the SNP continues to insist it would share the pound even after a “yes” vote.

The speech at the Olympic velodrome in London, where Scottish cyclist Chris Hoy won gold in British colours in 2012, marks a change of tack for Mr Cameron and is one of his most high-profile interventions in the separatism debate, as he made an impassioned plea to Scots: “We want you to stay.”

The prime minister’s pragmatic currency and devolution arguments in favour of resisting independence belied an otherwise emotional appeal to both Scots and those living elsewhere in the UK to fight for the United Kingdom in the coming months.

“This is our home, and I could not bear to see that home torn apart. I love this country. I love the United Kingdom and all it stands for,” he said.

“I will fight with all I have to keep us together. And so I want to be clear to everyone listening. There can be no complacency about the result of this referendum,” said Mr Cameron.

Alex Salmond, Scotland’s first minister and the face of the independence campaign, criticised Mr Cameron’s decision to give the speech in London, accused him of politicising the Olympics and called on the prime minister to hold a debate with him in Scotland.

“This is a speech delivered from London ostensibly telling the people of England what to do, instead of a debate the prime minister must do in Scotland with me . . . about the pros and cons of independence,” Mr Salmond said.

“Instead of a sermon from Mount Olympus . . . I want the prime minister to come and debate with me, instead of being a big feartie,” Mr Salmond told the BBC, using a Scottish slang word for a coward. “And then it’s game on.”

Mr Cameron admitted last month that interventions by a southern English Conservative prime minister might antagonise Scots and be counterproductive: “My appeal doesn’t stretch to every part,” he joked to MPs.

But senior Tories have been urging Mr Cameron to get more involved and the prime minister is now planning several visits to Scotland, including holding a cabinet meeting there this month. Mr Cameron has not been to Scotland since taking a holiday there last summer.

His move comes amid private Tory criticism last year of the “comatose” pro-union Better Together campaign led by Alistair Darling, the former Labour chancellor, and a realisation in Number 10 that the result could be closer than originally thought.

I want the prime minister to come and debate with me, instead of being a big feartie

A poll by TNS-BMRB this month found support for the Yes campaign on 29 per cent – reflecting a gradual creeping up of support for independence – with supporters of the 307-year-old union on 41 per cent.

The prime minister also defied those who warn he is too posh, southern and Conservative to enter the debate on Scotland’s future, to give his own personal account of the country’s importance to the union.

Mr Cameron said: “My surname goes back to the west Highlands. The name might mean ‘crooked nose’ but the clan motto is ‘Let us unite’ and that’s exactly what our nations have done.”

He also described Scotland as a “beacon in the North Sea”, invoking the values of freedom and democracy as integral to the idea of the UK.

“He speaks for a Westminster elite,” said Mr Salmond. “David Cameron . . . is the embodiment of why people should vote yes in September.”

The speech, made in the centre of the Olympic velodrome, made an undisguised effort to revive the patriotism inspired by Team GB in the 2012 Olympic Games, which saw passionate crowds in London cheering on Scottish athletes such as Sir Chris Hoy, the cyclist, and tennis player Andy Murray.

“For me, the best thing about the Olympics was the red, the white and the blue . . . it was the summer that patriotism came out of the shadows and into the sunshine,” Mr Cameron said.

Additional reporting by Henry Foy