BMG, which interviewed 1,466
Meanwhile 11% of those asked said England progressing in Euro 2016 would make them more likely to vote Remain.
The majority of those susceptible to the influence of football said a good England run would strengthen whichever side of the Brexit argument they were on.
Explaining the surprising results, Michael Turner, of BMG Research, thought the wave of patriotism would hit both Leavers and Remainers if England won, saying: "clearly there may be some sort of feel-good factor for both sides of the debate if England do well tonight."
Even more interestingly, the poll found a similar voting intent even if Britain crashed out of the Euros, which the Standard puts down to the fact that "Leavers may be more emotionally caught up in the EU referendum row."
Despite their feelings on Brexit, 63% of respondents said England manager Roy Hodgson should keep his job even if the team did badly from here on out.
At this point England would be unlucky not to make it to the knockout stages. The team needs to merely draw with Slovakia to guarantee a place in the last-16, but even if England loses it could still go through as one of the four best third-placed teams.