It has long been thought that Labour's Harold Wilson, ahead in the polls, lost the 1970 general election because England were dumped out of the World Cup by Germany four days before the vote.
"It deflated the mood in the nation," football journalist Keir Radnedge told the BBC. "Therefore, they looked for something new. Something new in that case was voting in a new government."
With England due to play their final Euro 2016 group game three days before the EU referendum, could history repeat itself?
Article continues belowThe Week
Escape your echo chamber. Get the facts behind the news, plus analysis from multiple perspectives.
Sign up for The Week's Free Newsletters
From our morning news briefing to a weekly Good News Newsletter, get the best of The Week delivered directly to your inbox.
From our morning news briefing to a weekly Good News Newsletter, get the best of The Week delivered directly to your inbox.
If England, Wales and Northern Ireland qualify for the knockout stages, "it will create a feel-good factor that could sway people to vote to stay in", the Daily Star predicts. However, an early exit will "have a fed-up public voting for Brexit".
Academics are divided about what the political effect of a "feel-good factor" might be, Henry Zeffman wrote in the New Statesman in February.
Some studies suggest that success in national sporting events "increases national pride, which in turn leads to greater prejudice against outsiders", while others "think that the country becomes more positive about the status quo", says Zeffman
It is also a matter of controlling the narrative, says Gordon Brown's ex-spin doctor, Charlie Whelan. He told the BBC that while the former Labour politician was in office, they would always avoid any political event clashing with a major football tie.
"If you have no idea what's going to happen on any given day, the agenda is set by 22 guys kicking round a football," he said.
With England fans fighting with Russian "ultras" and French police, this year's Euro coverage has competed with the referendum campaign for media air time, something Whelan says could complicate the Remain campaign's message.
The effect may be marginal, says Radnedge, but "marginal votes count in what may be a close-run contest".