Both the Tories and the Labour Party view Brexit as having been settled, although Labour has said it would renegotiate parts of the divorce deal to deliver a closer trading relationship with the EU.
There is no push from either party to reopen the question of EU membership.
But Beth Mann, political researcher at YouGov, said the new poll numbers suggested “there will likely come a point in the coming years when conversations about another referendum will be hard to avoid”.
She said: “Despite high levels of Bregret among the British public, this new polling shows that there is not necessarily a widespread appetite for another referendum anytime soon.
“However, there are strong party divisions that could swing campaigns as we head into the next election and beyond, with a significant majority of those who currently intend to vote Labour backing a referendum on re-joining the EU within the next five or 10 years.
“Our figures also suggest that if a referendum were to be held now, Britain re-joining the EU would come out on top. So, while political leaders have time on their side, this polling suggests that there will likely come a point in the coming years when conversations about another referendum will be hard to avoid.”
YouGov found that if a referendum was held on re-joining the EU some 50 per cent of people would likely vote to take Britain back into the bloc while 30 per cent said they would vote to stay out.
Remain voters are most in favour of holding a second referendum.
Some 41 per cent of 2016 Remain voters are in favour of holding another vote this year, 61 per cent want another referendum within the next five years and 70 per cent believe a re-run should take place in the next decade.
Among Leave voters, some eight per cent believe there should be a referendum this year, 16 per cent in the next five years and 20 per cent in the next 10 years.
A clear majority of Leave voters – 63 per cent – believe there should not be a referendum in the next 10 years.