The former Labour Prime Minister warned the UK Government that its tendency to present issues as Britain versus Scotland was "a losing ticket".
Mr Brown stressed it was imperative not to allow the Nationalists to set the terms of the debate along the lines of nationhood but that the choice was between two visions for Scotland's future: one he described as "patriotic", backing Scotland as part of the UK, pooling resources on welfare, defence and the economy; and the other as Nationalist, severing every single link Scotland had with the UK.
"Britain cannot be Britain without Scotland being part of the United Kingdom ... Britain and Scotland go together," said Mr Brown.
As both campaigns marked 100 days to go to the September 18 referendum, Mr Brown was asked at a lunch for Westminster parliamentary reporters whether Mr Cameron was a help or a hindrance to the No campaign.
"The Prime Minister has got to be involved in this debate. This is a debate about the future of Britain. It would be completely wrong if the leaders of the country were not involved."
He was then asked if Mr Cameron should take up the First Minister's challenge of a head-to-head debate. Mr Brown replied: "It would be a good idea if David Cameron could debate Alex Salmond, but I'm not involved in the negotiations."
Nationalists seized on the remark, claiming it was a "huge embarrassment" to Alistair Darling, leader of the No campaign, who maintains he is the person who should debate with the First Minister.
SNP MSP Annabelle Ewing said pressure was now building on Mr Cameron to agree to the head-to-head. She called on him to "show some leadership", and said if he failed then Scots would "come to the conclusion that he knows how weak his own arguments are and that he is feart to face the First Minister".
One senior Labour source was not best pleased with Mr Brown's support for a head-to-head, noting it went against his own criticism of a Britain versus Scotland approach, which a Prime Minister/First Minister clash would inevitably create.
No 10 sources responded coolly. They believe Mr Salmond's challenge is a political ruse to paint the referendum as a Scotland versus England battle and are adamant it "will never happen".
In a forceful intervention, Mr Brown said the referendum meant "Scotland is changing Britain for good".
Constitutionally, the idea of a unitary state or Westminster sovereignty is "dead and buried", he said, and has been replaced by popular sovereignty, with referendums deciding the big issues.
Mr Brown, MP for Kirkcaldy and Cowdenbeath, said Mr Salmond had made Scotland look "small" by unfurling a Saltire flag behind Mr Cameron when Andy Murray won the men's singles title at Wimbledon last year.
But Mr Brown also criticised the way Scots had been warned by the Treasury they would not be allowed to share the pound if they voted Yes. He also complained about "patronising" Whitehall publicity material suggesting Scots would be able to buy fish and chips every day for 10 weeks with the money they saved by voting No.
"Countries can be lost by mistake," he said, warning that presenting the referendum in terms of Britain versus Scotland would be "a losing ticket".
However, Danny Alexander, Chief Secretary to the Treasury, insisted the Government strategy had not come across this way, and it was in fact providing detailed information. "The polls and our own experience suggest people in Scotland want that and do not see it as divisive," he added.
Earlier, at a rally in Glasgow, Mr Darling urged No campaigners to match the emotion of the Yes campaign, while in Edinburgh Yes Scotland's Blair Jenkins said the pro-independence campaign was on course to collect one million signatures for its Yes Declaration pledge.
Elsewhere, a row broke out over the Yes campaign's "independence guarantee" card. Scottish Labour deputy leader Anas Sarwar said it was "full of assertions and mistakes".
Mr Darling, meanwhile, penned an article in the Evening Standard, telling Londoners: "The people of this great city have a deep interest in the future of our United Kingdom. If Scotland is torn away the effects will be felt throughout our islands."