British Prime Minister David Cameron evoked his own family's Scottish heritage as he set out an economic, political, cultural and emotional case for Scotland to remain part of the United Kingdom.

Mr Cameron warned that the world would lose "something very powerful and precious" if the UK's "family of nations" broke up forever.

Speaking at the Olympic Park in east London, Mr Cameron called on the people of England, Wales and Northern Ireland to send a message to Scotland as it prepares to vote on 18 September: "We want you to stay."

Independence would be bad for Scotland but would also leave the United Kingdom "deeply diminished" and would "rip the rug from under our own reputation" in the world, Mr Cameron said.

Separation would not only cost the UK some of its economic, political and diplomatic "clout" in the world, but would also tear up an "intricate tapestry" of human connections and relationships which mean that "for millions of people, there is no contradiction in being proud of your Scottishness, Englishness and Britishness - sometimes all at once".

Recalling that the name Cameron stems from the West Highlands, the Prime Minister said: "I am as proud of my Scottish heritage as I am of my English heritage.

"The name Cameron might mean 'crooked nose' but the clan motto is 'Let us unite' - and that's exactly what we in these islands have done."

Mr Cameron was accused by Scottish National Party Deputy First Minister Nicola Sturgeon of a "shameful" attempt to hijack the Olympic spirit for political purposes on the day when the Winter Games begin in Russia.

And Ms Sturgeon branded him "cowardly" for refusing to debate head to head with First Minister Alex Salmond.

The Prime Minister has previously acknowledged that his image as a "Tory toff from the Home Counties" does not make him a good figurehead for the No campaign in the referendum debate.

But he said: "Frankly, I care far too much to stay out of it. This is personal.

"Our great United Kingdom -  brave, brilliant, buccaneering, generous, tolerant, proud - this is our country.

"And we built it together. Brick by brick, Scotland, England, Wales, Northern Ireland, brick by brick.

"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. And I will fight with all I have to keep us together."

Warning supporters of the Union that they have only "seven months to save the most extraordinary country in history", he said: "Think of what we've done together - what we can do together - what we stand for together.

"Team GB. The winning team in world history. Let us stick together for a winning future too."