The Panelbase survey for The Sunday Times Scotland found that Scots are currently 53 per cent to 47 per cent in favour of staying in the UK.
However, backing for Scottish independence appears to grow in the event of the UK leaving the EU without a deal.
In that scenario, support for independence rises to 52 per cent and opposition falls to 48 per cent, the poll found.
Meanwhile, a majority (59-to-41 per cent) said they believe independence would be better for Scotland than a no-deal Brexit.
Panelbase surveyed 1,018 voters in Scotland from April 18-24.
The poll was published on the second day of the SNP conference in Edinburgh, where party leader Nicola Sturgeon is expected to declare it is “time for Scotland to become independent”.
It comes just days after Sturgeon, the First Minister of Scotland, told MSPs there should be another vote on Scotland’s place in the UK before the next Holyrood elections in May 2021.
On Saturday, a YouGov poll for The Times Scotland also recorded growing support for independence, with 49 per cent of Scots preparing to vote Yes, compared with 45 per cent in YouGov’s poll for the newspaper last northern summer.
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