We simply have no idea how many people will turn out to vote in the European Union (EU) referendum on 23 June. At the 2015 general election, there was a 66% turnout. In 2014's Scottish independence referendum, 85% of registered voters turned up on the day to cast their ballot. In the 2011 referendum on changing the electoral system to the Alternative Vote, just 42% turned out. But as anyone who works in the financial markets will tell you, past trends does not necessarily predict future participation.

With the EU issue burning hot, flamed by concerns over immigration in particular, and two fiery campaigns accusing each other of sowing fear and division with their rhetoric, are we set for a bumper turnout in the referendum like in Scotland? "It's difficult to accurately estimate what overall turnout will be as we don't experience referendums as often as we do general and other elections – so we're limited on points of comparison," said Glenn Gottfried, research manager at Ipsos MORI, a polling firm.

Ipsos research found 78% of Britons said they were certain to vote in the referendum. By comparison, 74% said the same ahead of the general election in 2015. "It's estimating the turnout levels for the various groups in society that will be important – will some groups be more motivated to vote in this referendum than they do at general elections?" Gottfried said. "Estimating this will be a challenge for all of us in the polling industry."

"Polls aren't necessarily the best way of predicting turnout," said Tom Mludzinski, director of political polling at ComRes, a pollster. "People tend to overclaim how likely they are to vote." He said ComRes anticipates the turnout will be similar to the last general election.

A survey of voters by the Electoral Reform Society, revealed turnout will hover around 57%. "It looks like the public are fairly sure this will be a sub-general election turnout level," said the group. But aware of the uncertainty about poll participation, and the risk of being caught off-guard, the Electoral Commission has told officials running polling stations to prepare for it to be as high as 80%.

"It's been said a lot that a lower turnout benefits leave and a higher turnout benefits remain," Mludzinski said. "That's a bit of an oversimplification." Why? Because some demographics are more likely to turn out than others. There are all sorts of factors that affect the likelihood of people turning up to vote — from wealth to education to age.

The pollster YouGov ranked groups of voters by those more likely to show up to vote. "Some of the key demographic groups who favour Brexit are indeed more likely to vote, but this is by no means true for all of them," wrote Joe Twyman, head of political and social research, on the YouGov website.

"Of 25 groups that were analysed, Ukip supporters were, for example, the strongest supporters of leaving the EU and were ranked second highest in terms of likelihood to vote. Similarly those aged 60 and above are the group with the second highest levels of support for leave and fourth in terms of likelihood to vote.

"The overall picture becomes more muddled, however, with the next three groups. Respondents from C2, D and E social grades, those not educated at university and those with low political interest all rank highly in terms of levels of support for Leave, but are near the bottom of the list when it comes to likelihood to vote."

EU referendum turnout polling YouGov
YouGov's breakdown of voting demographics, including their support for remain/leave and their ranking in a list of likelihood to turn out. YouGov

According to the Office for National Statistics (ONS), the total number of electors registered for parliamentary elections in the UK was 44,722,000 in 2015. There were 46,204,700 local government electors. Given the rush to get people registered before the deadline, which had to be extended by a day when the website crashed on the night registration was due to close, one can reasonably expect the number of potential voters to be at least similar to 2015.

Taking the middle number between those two, which is 45,463,350, and assuming a 60% turnout on that amount of registered voters, a single percent is equivalent to 272,780 people. So if there is, for example, a 53% vote for remain and 47% for leave, as shown by a NatCen poll released a couple of days before the referendum, the difference in the number of votes would be 1,636,680. Is this enough of a gap to answer the EU question indefinitely?

"Anything less than 60/40 puts it back on the agenda," Mludzinski argued. He pointed to the victory by 10 points for the Better Together campaign in the Scottish referendum. Since then, the Scottish National Party (SNP), which has pushed for independence for decades, is still performing well in domestic politics and there is already talk of a second independence referendum. The independence cause was not killed politically by the referendum defeat.

Perhaps factors beyond politics will affect the "knife-edge" EU vote, as NatCen described it. The police estimate that half a million British football fans will travel to France during Euro 2016. How many will be away on 23 June? And how many of those will have got around to casting a postal vote? Will the vote be close enough for it to matter?

Moreover, bad weather keeps people away from the ballot box — and Thursday's forecast looks ominous. Heavy showers are expected in London and the south east. "Increasingly warm and humid air will arrive from France later on Wednesday, bringing with it an increased risk of thunderstorms," says the Met Office. Trouble from the continent blowing across to the UK where rain could make all the difference — a very British end to a very British referendum.