While people in Scotland will make the decision in autumn next year, the implications will have obvious impacts across England, Wales and Northern Ireland, the Conservative leader said.
“Britain is admired around the world as a source of prosperity, power and security,” he said.
“Those glorious Olympics last summer reminded us just what we were capable of when we pull together: Scottish, English, Welsh, Northern Irish, all in the same boat – sometimes literally.
“If you told many people watching those Olympics around the world that we were going to erect barriers between our people, they’d probably be baffled. Put simply: Britain works. Britain works well. Why break it?”
Addressing matters of the “heart and head”, Mr Cameron spoke out one day before the British Government publishes the first in a series of analysis papers about Scotland’s role in the union.
It comes one week after the Scottish Government published a “road map” from the referendum next year to full statehood in early 2016.