A majority of Britons believe the Brexit vote increases the chances of the United Kingdom breaking apart, a new poll shows.

A survey by Opinium for the Observer shows that 54% agree that the UK’s vote to leave the EU has made a break-up more likely. Among Scots, the figure is even higher, at 63%.

The findings come days after Nicola Sturgeon, Scotland’s first minister, said there was a “cast-iron mandate” for a fresh referendum on Scottish independence.

The SNP leader said “the vote must take place within a timeframe to allow an informed choice to be made, when the terms of Brexit are clear but before the UK leaves the European Union or shortly afterwards.”

The figures are likely to make uncomfortable reading for the Conservative government. Theresa May, the prime minister, is already planning a tour of Wales, Scotland and Northern Ireland in an attempt to build a consensus before triggering article 50.

She has insisted that “now is not the time” for the referendum that the SNP had hoped to stage between autumn 2018 and spring 2019.

In 2014, Scots voted 55% to 45% to remain part of the UK in a divisive contest that heralded the emergence of the SNP as a serious political force, both in Westminster and north of the border.

Any future vote is likely to be closer, with 47% of Scots polled saying that they would prefer a yes vote in a new referendum, against 44% who prefer no. Scottish independence remains more unpopular in the rest of the UK, with 52% overall saying they would prefer continued union with England.

When UK adults were asked which party they trusted most to lead the negotiations, 35% chose the Conservatives – up from 30% in January and December. Only 12% said they trusted Labour and 10% Ukip.

May remains ahead of Jeremy Corbyn in terms of leadership ratings, with a net approval rating of 17%, against -36% for the Labour leader.

The Tories have maintained their 13-point lead over Labour in national voting intentions, with 41% saying they would vote Tory, compared with 28% for Corbyn’s party. Ukip is in third place on 13% (down 1 point), while the Liberal Democrats remain steady on 8%.

• Opinium Research carried out an online survey of 2,007 UK adults aged 18+ from 14 to 17 March 2017. Results have been weighted to representative criteria.