The 300th anniversary of Scotland's Union with England has been marked by renewed debate over the constitutional future.
The BBC poll showed that most people want the Union to continue
A poll for BBC Newsnight suggests that a majority in Scotland want the Union to continue, although others have suggested backing for independence.
The Scottish National Party (SNP) has renewed its calls for a referendum on the future of the Union.
However, Labour said separation was a "tired, old-fashioned idea".
The poll for the BBC's Newsnight programme indicated that 56% of people in Scotland would like the Union to continue as it is, with 32% wanting it to end.
However, some other recent polls which were worded differently suggested that voters might favour Scotland becoming independent in a referendum.
The Newsnight poll, which questioned 883 adults in England, 543 in Scotland and 527 in Wales, also indicated support on both sides of the Border for an English Parliament.
Another opinion poll published in The Scotsman newspaper suggested 36% of Scots believe that the Union has had a positive effect, while 27% think it has had a negative effect.
The SNP is launching a new campaign which will highlight May's elections to the Scottish Parliament.
It's poster declares: "1707: No right to choose - 2007: The right to choose."
SNP leader Alex Salmond said: "Those in the London parties who would deny the people their right to choose are the political reincarnation of the 'parcel of rogues' of 1707 who sold Scotland away.
"Over 80% of Scots believe that a referendum - putting the people in charge of the process - is the right way to decide Scotland's future."
A Scottish Labour Party spokesman said: "The Union has increased prosperity, stability and social justice in Scotland and indeed, throughout the UK.
"Separation is a tired, old-fashioned idea and the Labour Party will fight for every vote in the Scottish elections to defeat the separatists in the SNP who seek to impoverish Scotland with their obsession with constitutions."
Scottish Parliament Presiding Officer George Reid was attending a reception on Tuesday at Dover House, home of the Scotland Office in London, hosted by Scottish Secretary Douglas Alexander and Jack Straw, leader of the House of Commons.
It will see the launch of a commemorative £2 coin.
Mr Alexander said: "The United Kingdom has brought prosperity to the nations which formed it.
"Our nations have grown closer over the last 300 years with ties which are deepening still.
"Now half of Scots have family living south of the border and almost one in ten of the people living in Scotland were born in England."
Liberal Democrat leader Menzies Campbell called for a calm and rational debate on the role of MPs from the devolved nations.
"As Donald Dewar, the architect of the Scottish Parliament, made clear - 'devolution is a process not an event', for Westminster as well," he said.
Scottish Conservative leader Annabel Goldie said there was "no question" the Union had made Scotland and England stronger.
"It contributes massively to our culture, strength and prosperity whilst enabling us to maintain a proud sense of national and local identity," she said.
"Scottish Conservatives are the staunchest supporters of the Union.
"The wrong response, as presented by Gordon Brown, is to bully Scotland into remaining part of the UK through fear of the economic consequences of going it alone."