While Oldham West and Royton was voting – so overwhelmingly Labour – on 3 December, another vote was taking place not far away which may also have important consequences for the future of British politics. This vote was a referendum in Denmark on closer European cooperation on justice and security. And the result was that the No side won by 53 per cent to 47 per cent, and left Europe with a bit of a headache. The issues involved were technical, and the stakes seemed low to the Danish public. If you are arguing for a Yes vote on a technical question, explaining is more or less what you have to do, and, as Ronald Reagan said, ‘if you’re explaining, you’re losing’. The alternative is to run a campaign saying, ‘trust us, we’re the political establishment’, which is if anything an even less appetising proposition.

So let’s back up a bit. Why was this referendum called? Its origins date back to a referendum on the Maastricht Treaty in June 1992, in which the Danes rejected the treaty. The compromise agreed under the British presidency at the Edinburgh summit in December 1992 gave Denmark a number of opt-outs on parts of the treaty, and this was enough to get the revised package approved in another referendum in 1993. But while John Major was stitching together the Edinburgh compromise, a large number of Conservative backbenchers were calling for a ‘Fresh Start’ – using the opening created by Denmark to renegotiate other bits of Maastricht they disliked and expanding on the UK’s opt-outs agreed in the original treaty. The 1992 Danish referendum caused the simmering Tory row on Europe to erupt into the civil war that split the party in the 1990s and 2000s.

Denmark’s vote was on a package of 22 measures. Under the constitution, powers cannot be transferred to an international body without either a near-impossible 5/6 majority in parliament or a positive referendum vote, so what was proposed is to give pre-emptive approval to Denmark joining a number of European Union arrangements on security and criminal justice, subject to further approval by a majority in parliament. European-level involvement in these areas has grown considerably over the last 20 years and successive Danish governments, supported by nearly all the mainstream parties and most of the business and cultural establishment, have wanted to join. There is new urgency because the European police cooperation agency Europol is becoming a supranational rather than intergovernmental body in 2016 and Danish membership would lapse under the current opt-out arrangement. The newly elected minority conservative government decided to go ahead with the referendum early in its term, but the Yes lead eroded in the polls as the campaign has gone on, and by the end the outcome was not a surprise.

Even in Denmark, the referendum campaign did not set hearts racing. It was the eighth European referendum since accession in 1972, and there was weariness about another one even among party activists. The core arguments of each side were simple. The Yes (Ja) argument was that the police should be supported and strengthened and that European cooperation will help their work and keep people in Denmark safe from criminals and terrorists. The No argument boiled down to ‘No More EU’ – a simple dislike of supranational government.

The No (Nej) campaign was an otherwise incompatible alliance. The main force was the Danish People’s party, a rightwing populist group that polled well in the 2015 general election. Its brand of Euroscepticism would be familiar to most observers of the British political scene. The other part is a left/Green alliance which sees the EU as a global capitalist project that poses a threat to Denmark’s high standards of social and environmental protection. In this respect, Nej was rather like the ramshackle No campaign in the UK’s referendum in 1975. Left Euroscepticism has been in abeyance in the UK since the late 1980s, but it has shown recent signs of life because of the treatment of Greece, concerns over privatisation and the TTIP draft agreement with the United States, and the revival of traditional hard-left politics under Jeremy Corbyn. The UK’s Leave campaign will bring in many veterans of the No to AV campaign of 2011, which was a clever, mostly rightwing, organisation that gave disproportionate publicity to the supporters it had on the left; no doubt if a Eurosceptic left does not exist, one will be invented

The Danish campaign, as low-salience referendum campaigns tend to, wandered away from the question that the referendum vote will actually resolve. The Paris attacks, and the failures in coordination in Belgium that preceded it, might be expected to increase support for international policing; but they have also made Danes more jittery about securing their national borders. The No side raised the prospect that Denmark will be overruled on issues such as asylum and border control, something the Yes side hotly denies and regards as having been taken off the table by a political agreement prior to the calling of the referendum. Other apparently irrelevant issues were raised such as – bizarrely – allegations that Yes would lead to problems with equal marriage legislation and Denmark’s liberal attitudes to imprisonment and the age of criminal responsibility. It seemed a matter of throwing claims against the wall and seeing what stuck.

The Yes campaign was not without a few shrill moments. One Yes poster seemed to imply that voting No meant being soft on paedophiles, but Ja was more sinned against than sinning. The No side also used the technique, which will no doubt be applied in the UK, of deliberate synthetic outrage at any slight infringement by the Yes side or indeed official information; for instance, it complained about a government information website, leaving its much-publicised complaint until just before the campaign period, only for the information commissioner to make a little-noted ruling at the end of the campaign that there was nothing wrong with the official site.

The morning after: the Danish press can be pretty brutal

The Yes campaign lacked enthusiasm; even in the most pro-EU parties such as the Radical Liberals it has proved difficult to get serving politicians and party activists engaged in the campaign. It is a challenge to mobilise people for something they think is sensible, but not a burning issue, and for a proposition that involves either a fair amount of detailed knowledge or a degree of trust in political leaders to do the right thing. Yes was hampered by the neutrality expected from senior police officers – while they clearly want more cooperation on a European level they feel they cannot intervene in a democratic debate on how best to accomplish this.

The No campaign capitalised on feelings of distrust of the political elite and fears of change; it also argued that a No vote would not get in the way of police cooperation; separate arrangements could be made either for some sort of Europol associate status or coming back later for a specific referendum on Europol rather than the package. This has struck a chord with many middle-ground Danish voters, who feel that people of goodwill should be able to sort out a satisfactory solution in the circumstances and that one can pick and mix between the different measures. The Yes side argue that this relaxed attitude to the consequences of a No is mistaken; another referendum on a selective basis for Europol would require a treaty alteration because the package approach was part of the legal framework of the original opt-in. There is also no guarantee in these circumstances that the deal would be as good as that proposed today – there could be delays in access to data, for instance – and the Yes side does not trust the assurances of some of the No campaigners that they would support Europol in a subsequent single-issue referendum.

The result was a fairly decisive No. The national margin was 6.2 percentage points, and No won nearly across the board. The Yes vote was ahead only in Copenhagen city and the wealthy North Zealand hinterland of the capital. Even in Denmark, the political gap between the cosmopolitan, progressive urban centres and the rest of the country is apparent.

What does this mean for the UK? There is one possible immediate outcome. If the Danish government, and the rest of the member states, wish to allow the possibility of a single-measure referendum it could open a door for the UK government to demand treaty changes too to satisfy its own agenda, and – as in 1992 – for backbench Conservatives to ask for ever more concessions. It is rather different in that Major had a far more constructive approach to start with than David Cameron does; the Tories were then the Euro-allies of the mainstream Danish conservative Venstre party, while Cameron’s Tories are in league with the Danish People’s party, which drove the No campaign. The messy consequences could start as soon as tomorrow’s December European council meeting.

Further, the 2011 ‘referendum lock’ has created a situation where further expansions of EU competence would involve referendum votes on issues of similar boring complexity in Britain, with probably even lower turnouts and less illuminating campaigns. These sorts of referendum are anything but an exercise in deliberative democracy.

But before we get to that, there is the big referendum on whether the UK should be an EU member at all. The Leave campaign in the UK referendum will no doubt follow some of the same script as Nej – trying to limit the official information campaign, relativising arguments to unresolved ‘claim and counter-claim’, and promising that no bad consequences will arise because it can always be smoothed over afterwards in bilateral agreements. The Remain campaign needs to avoid seeming stodgy and establishment (gathering cross-party endorsements from the great and the good cannot be a principal focus, for instance), and be prepared to fight back in kind when attacked, or else its slim polling lead may slip through its fingers like the advantage the Yes campaign had in Denmark in September.

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Lewis Baston is a contributing editor to Progress and senior research fellow at Democratic Audit. He tweets @LewisBaston