Like many families, the debate has even divided newspaper siblings.
The Times and its sister, the Sunday Times, have chosen to support Remain and Leave respectively, the latter with the kind of editorializing that has come to distinguish it from its daily relative.
The other, more stark divergence is between the Mail titles.
In supporting Remain, the traditionally more liberal-minded Mail on Sunday has strongly challenged the Leave campaign with prominent reports about far-right infiltration. In contrast, the Daily Mail has been a stalwart supporter of the Brexit cause.
Things were very different in 1975, the last time Britain voted on this issue.
As Colin Seymour-Ure writes, every national newspaper endorsed staying in the European Economic Community with the exception of the Morning Star. It was a rare moment of press unity over the vexed issue of the UK's relations with Brussels.
Following World War II, most newspapers were broadly sympathetic to the formation of a common market that was seen as a force for stability and renewal.
There were, however, debates over British entry -- and when an attempt in the early 1960s failed, the Express couldn't resist proclaiming "Hallelujah!"
Yet the once-leading anti-EEC title's stance changed following the 1971 parliamentary vote in favor of British membership.
The Express subsequently joined rival newspapers in campaigning for continued membership in the referendum four years later.
The print media was perceived to have been a factor in moving the polls in favor of UK membership following a highly personalized debate. Pro-EEC papers characterized proponents of a "no" vote as scaremongers and the europhile Mirror labelled Tony Benn the "Minister of Fear."
Shouting across the Channel
Although there were perennial concerns over British contributions to the EEC budget, it would be the 1986 Single European Act that proved a watershed in press reporting on the subject.
Newspapers became increasingly fearful of Brussels and the issue came to the fore in late 1990 when the by now best-selling UK daily The Sun said "Up Yours, Delors!" to the European Commission president Jacques Delors and encouraged "its patriotic family of readers to tell the feelthy French to FROG OFF!"
It implored them to do so by shouting across the English Channel.
"At midday tomorrow Sun readers are urged to tell the French fool where to stuff his ECU [European Currency Unit]."
The prospect of closer union as well as a common currency meant jingoism was not confined to the "redtop" papers. One Telegraph report suggested a breakthrough in the Channel Tunnel's construction would allow the British to smell "the first whiffs of garlic."
Thatcher's 1990 downfall came in part after disagreements with colleagues over Europe that served to fuel Conservative divisions that had erupted after the Exchange Rate Mechanism (ERM) debacle two years later, when the UK had to pull out of the EU's fledgling monetary union after a dramatic run on the pound.
The Sun argued that "Black Wednesday" was a warning against the Maastricht Treaty's plan for what it denounced as a "United States of Europe ... deciding policies on tax, immigration and the economy with recourse to a Central Bank."
Together with other skeptical titles, the paper sought to discredit Brussels by publicizing what the commission dismissed as a series of eye-catching "Euro-myths" that included the 1994 classic: "Now They've Really Gone Bananas: Euro bosses ban 'too bendy' ones and set up minimum shop size of five-and-a-half inches."
The jocular approach subsided following the commission's 1996 decision to ban British beef due to heath concerns.
A front-page St George's Day Sun editorial, "EU THE JURY", demonized the union as a "beast ... which aims to devour our national identity" and "a very real dragon which threatens every single one of us throughout the United Kingdom," before declaring:
"A thousand years of civilization is being tossed away ... We want to see free trade between friendly nations, a genuine common market, not an Orwellian superstate which blindly tries to make Germans like Britons, or Spaniards live like Irishmen."
Rhetoric of this kind led Delors' successor Jacques Santer to attack the "anti-European propaganda, and even xenophobic propaganda, in the British press."
Battle for Britain
The European issue bedeviled the Conservative government with its internal divisions over the matter, which contributed to its defeat in 1997.
The Daily Mail had joined what it called the "Battle for Britain" in a front-page editorial attacking "the bipartisan omerta of the political elite" supporting further integration.
Material of this kind ensured the European issue became the major substantive policy debate during the 1997 general election campaign, even ahead of so-called "sleaze" and "education."
A year after Tony Blair entered Downing Street as the new Labour PM, The Sun was denouncing him as the "Most Dangerous Man in Britain" for his perceived pro-euro stance.
The issue once again featured prominently in the ensuing general election campaign of 2001. Despite formally endorsing a then seemingly unassailable Labour leader, The Sun took the unusual step of simultaneously praising opponent William Hague because of his anti-euro campaign to "Save the Pound."
The 2005 and 2010 general elections saw the European issue relegated down the print media agenda before it returned in 2015 following UKIP's victory in the previous year's EU poll.
By this time, leader Nigel Farage had helped ensure his party was associated with other related voter concerns, notably over immigration. Facing a perceived challenge from UKIP, the prime minister, David Cameron, promised a referendum on continued British membership.
His then ally, The Sun, also recognized the threat from UKIP when it ran a front-page endorsement of the Conservatives featuring "White Van Dan."
Dan had come to prominence after Labour politician Emily Thornberry tweeted a photo of his home bedecked with England flags -- she was savaged by many sections of the press for being out of touch with popular sentiment.
But, significantly, Dan Ware was quoted as supporting the EU and believing UKIP were "racist."
This did not dampen other papers' enthusiasm for UKIP or its leader.
Having dismissed the party as a "wasted vote" as recently as 2010, the Daily Express, the original skeptic journal, revisited its anti-common market roots by formally endorsing UKIP for the 2015 general election.
This stance has continued into the current referendum, with the Express providing the most pro-Leave coverage of any daily newspaper.
This stridency is characteristic of newspapers supporting Brexit.
The strength of these endorsements are also quantitatively rather than purely qualitatively different to those of the pro-Remain press: when circulation is also taken into account, over 80% of consumers who buy a daily paper read a title favoring British withdrawal from the EU.
Some believe the print media delivered crucial public backing for the EEC in advance of a 1975 poll that proved conclusive.
It remains to be seen whether and how newspapers might influence the outcome of a vote that appears to be on a knife edge.