The survey of people throughout the UK found that 62% wanted the union preserved, with just 38% supporting Scottish independence.
Only voters in Scotland will be able to have their say in September's referendum, but the poll for the Sunday Express found 58% believed people across the UK should be able to have their say because of the potential implications for the rest of the country, with 20% saying the decision should be left to the Scottish and 22% unsure.
The poll found Britons supported the cross-party stance adopted by George Osborne, Danny Alexander and Ed Balls ruling out a currency union with an independent Scotland.
Some 54% said the rest of the UK should not share the pound with an independent Scotland, against just 22% who backed sharing sterling.
The Vision Critical poll followed David Cameron's plea for supporters of the union throughout Great Britain and Northern Ireland to speak up in the debate.
The Prime Minister said there were "seven months to save the most extraordinary country in history" adding "this is our home, and I could not bear to see it torn apart".
The importance of the issue to voters south of the border was also highlighted by pop veteran David Bowie, who used his Brit award acceptance speech - which was delivered by supermodel Kate Moss - to say "Scotland stay with us".
But there was some good news for First Minister Alex Salmond in the polling data, with a narrow lead for independence among the small sample of Scottish voters polled.
Of the 188 polled who considered Scotland as their home nation, 52% indicated they supported the SNP's call for independence - 34% "strongly" and 18% "somewhat" against 48% who disagreed.
:: Vision Critical surveyed 2,060 British adults on February 19-20.