There have been several referendums that haven't happened in recent years, and they have all been more important in British politics than the one referendum that did happen, the one on the Alternative Vote in May this year.

Every year that he was Prime Minister, Tony Blair didn't have one on adopting the euro. According to Ed Balls, Blair wanted to but Balls wouldn't let him. This is not true, because Blair never got to the point where a referendum looked remotely winnable, and he was not one to hold a vote he might lose. He promised one on the European Constitution, but that document was killed off by earlier referendums in France and the Netherlands, called in a rush of blood to the head, now known as a "Papandreou", which were lost in 2005.

One of the first things Gordon Brown did as Prime Minister was not to have a referendum on the Lisbon Treaty, which the Constitution had become. David Cameron, in opposition, demanded one, but one of the first things he did in government was not to have a referendum either, for the pedantic reason that he had accidentally become Prime Minister too late and the treaty had already been ratified.

The most important referendum that won't happen, however, is not even going to not happen in this country, but is expected not to happen on 4 December in Greece. The proposed referendum, which frightened the markets while it seemed likely to go ahead (that is, between Monday and Thursday last week) has now stopped frightening the markets. But it will have an effect on the British politics of Europe for years to come.

It will strengthen Conservative Eurosceptics, who have just rebelled in record numbers over a demand for precisely what was briefly offered to the Greeks. What more evidence do we need that the governments of other EU countries are all run by agents of Douglas Carswell? When the Danes or the Irish vote the wrong way in referendums on Europe, they are made to do it again. Last week, the precious grail of direct democracy was offered to the Greek people and snatched away again when the markets predicted that they would give the wrong answer. It is as if the leaders of other EU countries are determined to treat the EU, and especially the eurozone, like a conspiracy of elites against the masses.

This is not simply a matter of looking bad, though. Daniel Finkelstein, executive editor of The Times and a friend of George Osborne, the Chancellor, wrote a significant article on Thursday – when it seemed that the Greeks would have a referendum. He pointed out that the closer integration of the eurozone, as advocated by Osborne and David Cameron, needs "popular consent".

The greater significance of Finkelstein's article, though, lay in his view that the Greek sub-crisis clarifies how the bigger euro crisis will change Britain's relationship with the rest of Europe. Whatever happens next "will change the terms of our membership and is likely to break the alliance that has always supported it" – an alliance that has included all three parties since Labour abandoned its policy of withdrawal in 1983.

It is an alliance that has held despite the rise of the Tory Eurosceptics, almost all of whom still favour continued EU membership. At most, there are perhaps 25 MPs, half of them Tories, who say publicly that Britain would be "Better Off Out".

Hinting that he himself now favours withdrawal, Finkelstein said, "There will – probably – remain strong arguments for being in the EU and much to be lost by leaving," before starting the next sentence with "But". The Chancellor's friend asked: "For how long will it remain the case that questioning Britain's membership of the EU will be something that cannot be done by a mainstream political figure?"

As if on cue, Ed Balls adopted what looked like a surprising Eurosceptic posture later that day. He said Labour would be against lending any more money to the IMF if it were to be used to bail out the eurozone. The Prime Minister may still find Balls "the most annoying person in politics" – he snapped at the Shadow Chancellor in the Commons last week for making his "flatlining" gesture – but it would be a big deal if Labour were to start a new zag in its long history of tacking on the European question.

Hugh Gaitskell opposed Harold Macmillan's early attempts to join the Common Market. Harold Wilson equivocated. Then the party wanted to stop the world and get off. Neil Kinnock reconciled it to a reality grudgingly accepted by the voters. Jacques Delors (for) and Margaret Thatcher (against) persuaded it that Europe was good because it was nice to the workers. Since then Labour (and the Lib Dems) have been enthusiasts, even, for a time, advocating Britain's adoption of the euro.

I am often surprised by Labour MPs, especially former ministers, now confiding that they have been Eurosceptics all along, and that they think there will have to be a big adjustment in Britain's place in Europe. That moment looks as if it will be upon us sooner than they expected. By "sceptic", they mean staying in the EU and renegotiating terms, the middle-way and least realistic of the options in the referendum on which the House of Commons voted recently.

But, if Finkelstein is right, the "in or out" question may become a mainstream one again. If the eurozone holds together, it will mean putting the UK and another nine EU members into a second-tier Europe, which will resemble the European Free Trade Association of the early days. If that happens, Britain's staying in the EU becomes much harder to defend. So it may be worth staying in only if the euro breaks up – the thing all European leaders, including Cameron, are desperate to avoid.

Either way, we may look back on last week's announcement of a referendum that was never held in Greece as a turning point in the British politics of Europe.

twitter.com/JohnRentoul; independent.co.uk/jrentoul