Should we beLEAVE that the Sun backing Brexit will swing the referendum outcome?

The answer is undoubtedly much less in the age of declining circulations, the growth of the internet and the rise of social media debate than was once the case. But it would also be foolish, as some psephologists and media academics would have us believe, to virtually discount the ability of newspapers to swing their readers' voting intentions one way or the other. And, in what increasingly looks like a volatile, unpredictable EU referendum outcome, that could yet prove a significant factor. Arguably more so in the context of a single issue choice between Bremain and Brexit than in the more complicated – but decidedly much less important for the future of the UK – context of a general election.

The Sun, of course, has been conspicuously Eurosceptic for the best part of four decades. Splash headlines like, 'Up Yours, Delors' and 'Hop off You Frogs' from the Kelvin MacKenzie era are part of tabloid folklore. In the 1975 referendum it urged its readers to vote to remain in the common market, only to change its mind within two years and its anti-EU mood music has never changed beyond varying volume levels.

No doubt the Sun's current editor, the canny Tony Gallagher, is convinced that today's splash reflects the majority sentiment of his paper's readership – boosted by a clutch of polls suggesting that Brexit has either now pulled ahead by 6 or 7 points or Bremain's once seemingly invincible lead of around 14 per cent has shrivelled to no more than a 1 per cent advantage.

Certainly Gallagher pulls no punches in a front page leader that I know clearly echoes his personal pro-Brexit conviction (although I don't doubt that he would have cleared it with Rupert Murdoch too). With a two-fingered wave at the 'establishment' (Rupert regards that as something of a personal badge of honour, despite those many years of cosy private meetings at Downing Street), the Sun pours a steaming bucket full of scorn on David Cameron's 'witless' assurances about the benefits of Remain.

The Sun said: 'We must set ourselves free from dictatorial Brussels...if we stay, Britain will be engulfed in a few short years by this relentlessly expanding German dominated federal state....Our powers and values will be further eroded......Staying in will be worse for immigration, worse for jobs, worse for wages....worse for our way of life.....To remain means being powerless to cut mass immigration which keeps wages low and puts catastrophic pressure on our schools, hospitals, roads and housing stock....Once we reassert our sovereignty, embracing a future as a self-governing, powerful nation envied by all, we will be able to pick and choose the best migrants from the whole world....Outside the EU we can become richer, safer and free at long last to forge our own destiny, using our enormous clout as the world's fifth biggest economy, strike deals with the other 85% of the world.'

The Sun splash also branded the Remain campaign effectively headed by David Cameron and George Osborne as being 'made up of the corporate establishment, arrogant Europhiles and foreign banks who have set out to terrify us about life outside the EU'. (It is interesting to note that the barnstorming front page leader did not appear in more pro-Remain Scotland where only a straight single column news story on Brexit's rise in the opinion polls figured on page one.)

To those of us in the remain camp, it conjured up an image of Boris, Gove and even Farage peeking over the author's shoulder as he tapped the keyboard, even though I don't doubt the words are the creation of Tony Gallagher and his in-house leader writers. Almost certainly with a nod of approval from the wings from Rupert himself.

So does the Sun's first out of the trap declaration signal a full-scale show of support from the Murdoch UK titles for Brexit – a move which probably would send the prime minister closer to depression and panic? On that, I'm rather more doubtful than some Murdoch watchers. If you analyse the Times and Sunday Times coverage and leaders of recent days, there lurks the suspicion that at least one of them (probably the Times) could yet (grudgingly) back Remain on the basis of the economic future of the UK, while demanding that Cameron must fight on for greater EU reform, something a desperately narrow win for Remain might just help concentrate the minds of other (relieved) EU leaders.

Elsewhere on what used to be Fleet Street, there looms the intriguing prospect of the Daily Mail, whose leaders have been even more scathing about Cameron, Osborne and the Remain argument, almost certainly formally endorsing Leave, while its stablemate the Mail on Sunday has been dropping leader column hints and carrying enough pro-Remain guest articles to suggest it will go the other way to its daily sister. Quite how that would play in the relationship between editor-in-chief Paul Dacre and the MoS's ambitious editor, Geordie Greig, is the stuff of much wine bar gossip down Kensington way.

The Telegraph titles look set to swing toward Brexit, although without quite the vigour and vehemence of the Sun today and the Daily Mail's anticipated line. The Mirror, the Guardian and the Observer can be counted on to back Remain despite their dislike of a Tory government, but in readership/circulation terms are heavily outgunned by the pro-Tory but anti-Remain prints. While the online-only Independent will almost certainly be pro-Remain, unless it decides against declaring a formal editorial position.

Meanwhile a fascinating research study a few days ago by Loughborough University into referendum media coverage has thrown up some fascinating and potentially significant stats – particularly regarding the broadcast media which, of course, cannot – by statute – adopt the partisan stance of the print world. Jeremy Corbyn (in 10th place) was the only Labour politician to figure in the top ten of politicians in coverage terms.

In short, both broadcast and newspapers' fascination with the (admittedly) 'sexier' story of 'Blue on Blue' civil war, the fate of David Cameron and the ambitions of a certain blond bombshell had eclipsed coverage of pro-Remain Labour figures and the Labour party's efforts on the campaign trail.

And certainly in print – but often on the airwaves too – Jeremy Corbyn's speeches were arguably underplayed and frequently underpinned by references to the Labour leader's anti-EU history and suggestions that he's at best now a lukewarm 'convert' for Remain.

At this point, let me make it clear that I'm a pro-Remain, but non-Corbynista, lifelong Labour supporter who believes that, for all its many faults, staying in the EU represents the safer option for the UK's future in terms of our economy, our security and our status in the world than a gigantic leap into the unknown. And if Boris Johnson and Michael Gove want to accuse me of clinging to nurse for fear of something worse, so be it.

By coincidence or not, the Sun nailed its colours spectacularly to the Brexit flag just as David Cameron took a deliberate back seat and Labour – whose supporters really are the key to the result on 23 June – picked up the baton. A major speech by Corbyn, flanked by most of his shadow cabinet and many of Britain's trade union leaders, pleaded with Labour voters to back Remain, citing the prospect of huge job losses, the threat to wages and workers' rights and the weight of economists’ warnings about the dangers of another recession and worse.

It came against the depressing backdrop of those polls showing Leave ahead and many Labour voters confused over the party's official position on the referendum, with far too many for comfort suffering the misapprehension the party is actually pro-Brexit. Not to mention those working class Labour voters in some heartland areas where the immigration issue is swamping everything else, including economic common sense, and where the UKIP factor will be the elephant in the polling booth.

Some Labour leaders, including Angela Eagle, one of its better campaign trail performers, complain bitterly to me that a 'media obsession with Blue on Blue in-fighting has screwed coverage undemocratically'. Yes, they have a point... but complaining about brutal reality isn't going to keep the UK in the EU. And the barrage of anti-Remain artillery fire from much of the country's biggest newspapers isn't going to ease up.

With just a week to D-Day to go, Corbyn and his front bench team and Britain's trade union bosses have to pull out all the stops in a last-ditch effort to win over Labour waverers and mobilise their ground troops across the country as if this were another general election. The natural temptation to give David Cameron a bloody nose among some Labour voters becomes the equivalent of shooting yourself in the brain if the result is economic catastrophe and the emergence of a far more right wing Tory government headed by Bojo, Gove and IDS.

With the spectre of defeat looming, Corbyn might even be wise to reconsider his refusal to share a platform with David Cameron on the televised campaign trail rather than leave it to the likes of Harriet Harman to stand alongside the prime minister and argue the cross-party, national interest case for Remain.

There are those on Labour's far left who argue that victory for Leave would lead to economic collapse and the breakdown of civil society on a scale that would lead eventually to an overwhelming Labour election victory. Even if they were right about the first bit, Labour's natural supporters would suffer more than anyone and would be far more likely – with hindsight – to blame Corbyn and the party leadership of the EU referendum campaign 2016 for their woes and the grim future facing their children and grandchildren.

The insouciance with which Boris, Gove, Farage shrug off warnings signs such as the sharp fall in the £, the £60bn plus fall in the value of FTSE shares and the opinions of those derided experts from the Bank of England, the IFS, the WTO, IMF and other assorted acronyms ought really to send a shudder down voters' spines. Not least among those with Labour sympathies. But, for the moment at least, Brexit campaigners – with the aid of media cheerleaders – are successfully selling the notion of over-simplified patriotism and immigration fears above hard economic truths and the marked absence of a coherent pro-Brexit economic strategy for the UK is in danger of escaping voters' detailed attention.

Optimists – some inside Labour's hierarchy – still anticipate that, as in the Scottish referendum, there will be a late swing back to the safety of the status quo, especially among the currently undecided. They may well be right, but if the latest opinion polls are correct (and, OK, that's a big question in itself) the gap may be widening too much to pull back without a superhuman effort by the Labour leadership to support Cameron – much as that might stick in Corbyn's craw.

A couple of weeks or so ago I'd have bet my best shirt on Remain winning on 23 June. Today I'd only gamble a pair of socks, the ones with the small hole in the toe. And how much the media debate – whether in partisan print or TV studio debate – shapes over the last few days could yet prove pivotal.

Paul Connew is a media commentator, broadcaster, former editor of the Sunday Mirror and deputy editor Daily Mirror