The big EU referendum story of the last couple of days has been the revelation, if that’s the word, that migration from the Union to the UK appears substantially higher than was previously admitted.

After being pressed on why the number of National Insurance numbers being issued to new arrivals was much higher than the number of officially recorded immigrants, the ONS has claimed that short-term visitors (who stay less than one year) account for most of the shortfall.

The result has been predictable enough: pro-Leave outlets have seized upon a conspiracy of silence, and pro-Remain papers are maintaining that people who go home after 12 months are unlikely to be a burden on the UK.

Immigration is obviously a subject which has been increasingly important in British politics for some time, with debate raging over whether its undoubted economic benefits outweigh the cost to low-skilled Britons, who are said to face stiffer competition, over-worked public services, and depressed wages.

Yet for all the noise, we may be about to see just how important immigration actually is to the electorate.

For better or worse, Remain clearly feel that they are winning on the economic front. The best of the Leave campaign might have ambitious and outward-looking messages about deregulation and global trade, such as those set out in Martin Durkin’s Brexit: The Movie.

But Remain can wheel out any number of big businesses, economists, and now the Governor of the Bank of England to warn that leaving the EU spells doom and gloom. With a cautious electorate and the normal dynamics of a plebiscite weighted towards the status quo, that seems (tactically, at least) the stronger hand.

As constitutional matters like sovereignty, whilst important subjects of debate, scarcely energise the electorate, that does leave immigration has one of the main pillars of the Leave case.

That fact alone doesn’t necessarily prescribe a certain type of campaign: Vote Leave were probably right to eschew Nigel Farage’s base-friendly campaign in exchange for a model which engaged with – and wouldn’t put off – swing voters.

EU membership does mean that we can’t stop citizens of other EU countries from moving to the UK – and that includes those millions whom Angela Merkel has invited in and who will in time, presumably, be offered German citizenship. Meanwhile our renegotiation has shown that we can’t stop them claiming welfare.

(Whether or not you believe that many of them actually claim welfare matters no more than whether you genuinely believe quitting the EU risks World War Three).

The public regularly express their deep dissatisfaction with this to pollsters and politicians, and rank it as one of, if not the, most important political issues. This is their best chance in a very long time to do something about it.

Regardless of the campaign we might like to have seen, between now and polling day most voters will likely be weighing Remain’s gloomy economic prediction with Leave’s case for border control. Then we’ll find out how important the British public think immigration really is.