In his highest-profile intervention yet in the debate on Scottish independence, the Prime Minister warned the world would lose "something very powerful and precious" if the UK's "family of nations" broke up forever.
In the speech, co-hosted by Glasgow Caledonian University as part of a speakers' series, he urged the English, Welsh and Northern Irish to pick up the telephone and ask their loved ones north of the Border to vote No.
Scotland's First Minister Alex Salmond accused Mr Cameron of making a "bogus" argument and repeated his challenge for the Prime Minister to agree to a head-to-head debate on the issue.
As well as raising fears of the emotional impact, Mr Cameron also warned against the SNP's plans for a currency union, saying it would be "extremely difficult" to make it work.
However, speaking at the Olympic Park in London, he said that while economic arguments were important, for him "that's not what it's really about".
He said: "It's about the slave who escaped his master after the American Revolution because he was offered liberty and land by the British crown. In gratitude, he renamed himself this: British Freedom.
"It's about Lord Lovat on the beach on D-Day, the bagpipes playing as his brigade landed ashore."
He added: "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."
Recalling the name Cameron stems from the West Highlands, the Conservative leader said he was proud of his Scottish heritage and pointed out that the clan motto is "let us unite".
He also defended his decision to make the speech in London, saying he planned to make similar rallying calls across the UK.
He pointed to his Aberdeen trip later this month, which will see the cabinet meet in Scotland for just the second time in its history.
Yes Scotland chief executive Blair Jenkins accused him of "continuing to lecture Scotland".
First Minister Alex Salmond said: "David Cameron said he will 'fight with all he has' against Scotland's independence - but that doesn't extend to having a head-to-head debate on the subject.
"He says his appeal is to the people of England, Wales and Northern Ireland - but his Government makes policy for of all of the UK, including Scotland, and he cannot keep dodging that debate.
"In two weeks' time, the UK Cabinet and the Scottish Cabinet are meeting in the same city at the same time. Let's have that rumble in the jungle, a dust-up in Dyce.
The event was timed to coincide with the opening of the Sochi Winter Olympics in Russia.