Brexit will change far more than our relationship with the European Union. Just look at the government: take one profoundly divided political party. Call a referendum on the very issue that most divides it (apparently in an attempt to unite it). And lose. Then, sit back, relax, and watch the horror show that is the contemporary Conservative Party unfold.

To be fair, neither of the large political parties have found Brexit easy to cope with, and for good reason. The issue divides the electorate along unfamiliar lines. Elections have, at least until earlier this year, been fought along left-right lines – focusing on questions related to the role of the state in the economy. The parties distinguish themselves along this axis.

Brexit, however, cuts in a totally different direction. Insofar as it can be associated with any set of issues, these are ‘values’ issues, such as respect for traditional attitudes towards crime and punishment, censorship and authority. And this division cuts through normal allegiances, as the recent election made all too clear. We live in a post-referendum world in which Stoke South votes Tory, while Kensington and Chelsea fell to Jeremy Corbyn.

Yet the problems, particularly for the Conservatives, run far deeper. Brexit marks the culmination of half a century of civil war within the party over Europe. This broke out at the time of the Maastricht treaty which took European integration beyond the single market that Margaret Thatcher had pushed so hard for, creating a ‘European Union’ and ushering in cooperation in foreign and security policy, home affairs, and, of course, creating a single currency.

Debates over the treaty saw repeated back bench rebellions, while the 1992 election witnessed the election to parliament of several of those who were to play prominent roles in the referendum 24 years later (take a bow, Iain Duncan Smith and Bernard Jenkin). And during those years, Europe continued to haunt the party, notwithstanding David Cameron’s plea that they stop banging on about it.

So there are grudges to be settled. And this in part explains the bitterness that is all too visible not only in the parliamentary party, but in the Cabinet itself. These division are already happening Theresa May’s attempts to negotiate Brexit. Press reports suggest she has not even discussed the nature of a final deal with her Cabinet as yet, so busy are they squabbling over the ‘divorce bill’ and the role of the European Court of Justice in any transition.

So far, so serious, yet there is more. Because apart from the profound and deep seated differences of opinion within the party over the EU itself, Brexit has proven the catalyst for the emergence of serious divisions about economic policy that cut across the Brexit divide.

Think back to Theresa May’s manifesto, arguably the most statist and interventionist produced by a governing party in living memory. It declared that Conservatives ‘do not believe in untrammeled free markets. We reject the cult of selfish individualism. We abhor social division, injustice, unfairness and inequality.’ No wonder the Spectator Magazine was moved to label the Prime Minister the most left-wing leader the Tories had had in 40 years.

Yet her approach did not appeal to all sections of her party. For some, talk of workers’ rights, of limiting the free market, of price caps and the like was little short of heresy. There were many in the ranks of the Conservative parliamentary party who did not exactly weep when the contents of that document were consigned to the rubbish bin.

Yet the issues will resurface in the context of Brexit. Take agriculture. One consequence of the decision to leave the European Union is that, free of the Common Agricultural Policy, we will need to define our own policies. For some in the party this is an unparalleled opportunity to cut subsidies, to stop paying money to farmers and allow the market to take its course. For others, often in rural constituencies, such thinking smacks of electoral suicide. It is more than likely that the Government will choose to adopt a holding pattern, keeping things as they are for the time being in any new national agricultural policy, but the debate will have to be had.

And of course, lurking behind all this is the million-dollar question. How can the party engineer a Brexit that does not fatally damage its reputation for economic competence? Europe cost it this reputation before, remember. On 16 September 1992, Britain crashed out of the European Exchange Rate Mechanism (ERM). Despite spending billions of currency reserves and raising interest rates to a giddy 15 per cent in an attempt to prop up sterling, the government proved unable to keep the pound above the lower limit set for it within the Exchange Rate Mechanism.

All indications are that was is to come will prove much worse. There are very few serious economists who do not believe that leaving the single market and the customs union will prove economically costly. The current gung-ho confidence of the Brexiters in the cabinet will make the cold reality of this all the harder to explain away. Little wonder that the Prime Minister is desperate for transition (albeit that she insists on using the misnomer of ‘implementation phase’). This might, at least, postpone the economic reckoning.

What it will not do is heal her party. The two divisions – over Brexit and the economic policies to accompany it – are too profound, too entrenched. And they cannot be finessed. The next couple of years will require clear decisions and binary choices.

The Brexit effect on our politics has been, and continues to be, profound. As the party that was largely responsible for it is about to find out.

Anand Menon is author, with Geoff Evans, of "Brexit and British Politics", published on 27 October by Polity.