The survey by Savanta ComRes found if the referendum was re-run today the result would be a narrow win for Remain – by 51% to 49% – if undecideds are discounted.
That compares to the actual result in June 23 2016 poll of 51.9% for Leave to 48.1% for Remain.
However, if the question was put differently with the choice of the UK rejoining the EU, the result would be reversed with 51% in favour of staying out.
The poll found very little switching of views over the preceding five years with just 6% of Remainers in 2016 saying they would now vote Leave, and 7% of Leavers supporting Remain.
Around a third of respondents – 31% – said Brexit has been a success, while slightly more – 34% – regard it as a failure.
More than half – 51% – said it had left the country more divided with just 13% who thought it was more united.
The polling firm’s political research director Chris Hopkins said: “On the five-year anniversary of the Brexit vote, this poll shows a country just as divided as it was during the campaign, with a re-run of the referendum on a knife-edge according to this voting intention.
“However, if either of these questions were to be put to the British people again, those who did not vote in 2016 look to be a key source of Remain/Rejoin support, and there are always likely to be sceptics regarding whether such potential voters would even turn out in any future vote.
“Therefore those still in favour of Remaining or Rejoining would need to do much more to convince Leavers that they’d made the wrong decision in 2016, rather than relying on those who did not vote last time to turn out.”
– Savanta ComRes interviewed 2,191 UK adults aged 18 and over between June 18 and 20.