Support for the present constitutional set-up was at 68 per cent in England and 52 per cent in Scotland, a poll for the centre-right Policy Exchange think-tank found.
But there is concern over the impact of Brexit, with 59 per cent of Scots claiming the departure from the EU could make the break-up of the UK more likely.
The survey also found Scots are most likely to identify more with their home nation than with the UK as a whole, with 44 per cent of English, 60 per cent of Scots, 49 per cent of Welsh and 51 per cent of Northern Irish saying that they are identifying more with their home nation than with the UK as a whole in recent years.
Policy Exchange, which has close links to the Conservatives, was set up in 2002 and advocates free market solutions to social problems.
Policy Exchange director Dean Godson said: “Support for the Union is strong – but people are understandably nervous about the future. The UK needs a ‘new Unionism’, one based not just on the constituent parts of the United Kingdom, but on the regions and peoples within them.
“A new Unionism would not deny the difficulties faced by the United Kingdom, but Brexit also provides an opportunity for a reboot of one of the most successful nation-states in modern history.”
Scottish Conservatives leader Ruth Davidson will be among the speakers at a Policy Exchange event in London today. She will join Michael Gove and former Scottish Labour leader Jim Murphy among other speakers in discussing the future of the Union.