The authors of the survey in a communiqué, claim, "We now estimate that the United Kingdom would vote to stay in the European Union by a majority of 54% of the votes against 46%" in favour of leaving.
However, while it was backed by 63% of people who voted Remain, it was backed by just 20% of Leave voters. In Orkney it is even smaller at 29 per cent.
She said: "Apparently, this is a survey that has been conducted of 20,000 people".
Speaking during the Channel 4 debate Brexit: What the Nation Really Thinks, former UKIP leader Nigel Farage said: "This is a room full of Remainers, on the panel - Remain, Remain, Remain, four Remainers, they're not making the Brexit argument".
The talks could extend into December, but Theresa May would rather avoid this scenario as it would ensure that there would be no chance of securing the parliamentary vote over or before Christmas.
Scottish National Party Shetland branch chairman Iain Malcolmson said that many folk he had talked to had changed their minds since the referendum.
Malcolmson said that far from reflecting the will of the people, the figures showed that a clear majority were now in favour of remain.
The Times also said Mrs May's on course to get an agreement on a future economic partnership that will let Britain keep open the prospect of a similar free trade accord to the one Canada has with the European Union - a move it said could help persuade the euro-sceptic Tories to back the deal.
The move comes as May is believed to be closing in on a deal with the European Union (EU) over an insurance plan, or "backstop", meant to avoid border infrastructure between Northern Ireland and the Republic of Ireland.
"The house of commons needs to do its job and that is not being helped by the incompetence of the Conservative government". The results indicated the Leave vote would slide to 46 per cent.
"Democracy is a process, it's not an event".
Lidington also said the British government would stand by the written commitments it had already made on the backstop, which include an agreement that it would apply unless and until a better solution is found.
Ms O'Neill commended the letter signed by 1,000 nationalists across Ireland to Mr Varadkar, urging him to defend the rights of Irish citizens north of the border amid uncertainty caused by Brexit and Stormont's political crisis.
"I don't speak for nor do I know every single person that voted Brexit, but what I do know is that every single person that I know voted Brexit would still vote Brexit tomorrow".