We all know families who fight and argue in the privacy of their own homes but put on a flawless display in public. So it was, for a few days at least, with the Conservative Party when the campaign for the EU referendum began. Both sides were keen to keep it that way, in the long-term interests of their party. Last month, one MP dressed down Norman Smith, the BBC political reporter, for going on the airwaves and talking about “the Tory civil war”. At that stage, he was perhaps right to do so.

Tempers are, however, beginning to fray. Members of White’s, the St James’s Street club and a foremost lair of the Tory grandee, were recently alarmed to see two of that species, Nicholas Soames MP and David

Heathcoat-Amory, an MP until 2010 and a former Europe minister, going at it hammer and tongs about the European question during the lunch hour. Anyone familiar with Soames’s entertaining Twitter feed, which is currently devoted mainly to savaging fellow Tories in Vote Leave, will know that he is no stranger to technicolor vituperation.

It was, according to the account doing the rounds, a ferocious argument, though no blows were struck. “Nicholas and David have known each other since school,” a friend of both men told me. “They have more in common than separates them. It just shows how fraught things are.” That is certainly true. I well remember Soames, a lifelong pro-European, expressing his genuine dismay that Heathcoat-Amory was defeated in 2010 because a Ukip candidate, standing ironically against a devoutly Eurosceptic Tory, split the vote in his Wells constituency and let in a Lib Dem.

Another MP, using an appropriate public school metaphor for a gentlemen’s club packed with Old Etonians, likened them to boys who are friends but who, once on opposite sides of the sports field, let all hell loose at each other. One does not doubt that Soames’s and Heathcoat-Amory’s regard for each other will survive the referendum. Whether the same can be said for the two sides of the Conservative Party – unequal sides at that – come 24 June is quite a different matter.

The way David Cameron has conducted his wing of the Remain campaign in recent weeks has horrified many Tory MPs, even some who are or were notionally on his side. “The personal attacks and crude propaganda have really upset the party and I don’t think he understands how badly this has gone down in the constituencies,” a Remainer told me.

The personal attacks are certainly out in force. Downing Street has started to brief the media about those in particular disfavour. The Sunday Times reported on 15 May that Priti Patel, the employment minister, had behaved “appallingly” (her crime seemed to have been pointing out the government’s failure to supply enough school places to cope with the recent influx of eastern European immigrants). It also claimed that Cameron was especially angry with Michael Gove – which, since Gove has behaved with politeness and a complete lack of hysteria towards the Prime Minister, suggests that the latter must have a very thin skin indeed. Gove does annoy Cameron and his friends, not because of bad behaviour but because his detailed and measured analysis of what is wrong with the EU is hard to rebut, in contrast to more emotive outbursts by the likes of Boris Johnson that can be swatted aside.

Meanwhile, Cameron has sought to ridicule Bernard Jenkin, one of the most vocal Leavers among MPs, for making a perfectly reasonable observation about the dilution of trade union legislation in return for the unions’ support of Remain. The snide side of the Prime Minister’s character, depressingly familiar to those who deal with him in private, is becoming more and more unchecked as tensions in the campaign rise. There have also been briefings against

Penny Mordaunt, the armed forces minister, and, of course, Johnson. One attempt to terrify the country was to have the Sunday Times splash that, Brexit or not, Johnson would be the next leader and, therefore, prime minister. Downing Street seems not to realise that such an outcome is, for reasons few can fathom, one the general public seems to want.

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The Tory party has long been a coalition. Most diehard Leavers had no social or personal relations with their colleagues in Remain anyway, so that has not changed. Any breakdown in civilities among others at the moment is, for the most part, temporary. Many take the view of Jacob Rees-Mogg that the result must be binding whatever it is and the party must move on. Equally, many don’t, and if the outcome is a narrow victory for Remain it will be the worst possible result for the Prime Minister.

Those trying to maintain peace in the parliamentary party – and it is important to note that a few dozen MPs have never really been interested in Europe and are showing little interest now – believe that things could have been worse. Veterans say the atmosphere is better than it was during the Major government, in the arguments over the ratification of the Maastricht Treaty and Britain’s inglorious departure from the Exchange Rate Mechanism. That, too, is probably true, when one recalls that nine MPs had the whip withdrawn, John Major described some of his cabinet colleagues as “bastards” and he felt constrained to call a leadership contest to prove his mandate to lead the Tories. However, the vote is still a month away and there is scope for things

to worsen.

With the government and the Whitehall machine distracted by the referendum, other aspects of Conservative rule are causing irritation within the party. There is a sense that the whips and Downing Street have given up trying to take MPs with them on other issues, or to explain why changes of policy are being made. There is little doubt about the fragility of the economy, or that it could go south even if the UK remains in the EU – and George Osborne is felt to be doing too little to demonstrate the proverbial firm hand on the tiller, or to inspire confidence among his colleagues.

The recent U-turn on academy schools has caused particular rage among MPs who had gone to great lengths to explain and defend the previous policy to their constituents. Now they find themselves having to do the opposite and, as one of the less self-regarding said to me, “No pompous Tory MP likes being made to look stupid.” There is a widespread belief even among the more feminist MPs – and, believe it or not, the Tories have them of both genders – that Nicky Morgan has proved she is nothing more than a token presence in the cabinet.

Speculation about what would happen in the event of Brexit – and none of the 20 or so MPs I spoke to in preparing this piece, whatever their allegiances, would rule it out – is now starting to grip the Conservatives and is causing tempers to rise. Nobody seems to want Cameron’s immediate departure if the vote goes against him. There is talk of a “managed, orderly withdrawal” to see the party and the country through the initial shock of the change, with a contest getting under way formally at the Tory conference in October and the process – a vote of the parliamentary party, followed by a plebiscite of the membership to decide between the two most popular candidates – over by early December.

Johnson’s high-profile Brexit campaign is, in effect, the start of his bid for the leadership and why Cameron is so agitated about him. Johnson, as I wrote here in March, has not made the best impression on his fellow MPs since returning to the House last May and it is far from assured that he will be one of the final two candidates. There is also an uncomfortable recognition that he achieved little for London as mayor, other than traffic chaos and a series of vanity projects. “We’d like to do a Checkpoint Charlie-style swap, halfway across Westminster Bridge, with Sadiq Khan,” a Remainer told me.

However, Tory activists forcefully tell their MPs that Johnson is a “winner” who merits support in a leadership vote. Some younger MPs, yet to learn the difference between being a representative and being a delegate, are nervous of disagreeing. Three of them – Nigel Adams, Ben Wallace (a junior Northern Ireland minister and former soldier) and Jake Berry – are running a campaign for Johnson, organising lavish drinks parties for colleagues so the candidate can press the flesh. This irritates older MPs, who see it as a provocative manifestation of ambition and vulgarity that the party could do without.

A prominent Brexiter is almost certain to be in the last two in the leadership contest, be it later this year or in 2019-20, whatever the outcome of the referendum. Whether that is Johnson depends on if he self-destructs during this campaign – his reference to Hitler in his Sunday Telegraph interview on 15 May suggests that is quite possible, given the opportunities ahead. What might entertain the general public – and his unrestrained remarks, such as about President Obama’s Kenyan heritage, probably do –

increasingly angers his colleagues.

It may then be up to Michael Gove to offer himself, something that is said to be unlikely at the moment but that may become less so if things go badly for Johnson. Whatever Cameron thinks of his Justice Secretary, his colleagues have nothing but praise for the way in which he has conducted himself. It is widely thought that, in the event of a Remain victory, Cameron will promote Gove, possibly even to deputy prime minister, as a very public healing of wounds, in an attempt to unify his fractured party.

The favourite to end up in the last two with a Brexiter if there is an early leadership contest is Theresa May, described by one who knows her well as “cold, unfriendly, charmless, not as clever as she thinks she is, lacking imagination, unable to think outside the railway lines and intellectually dishonest”. However, he said that were the choice to be between her and Johnson, “I would, of course, vote for her.”

The wider party probably would not. It is accepted that if Johnson reached the last two, the party in the country would elect him leader. His fate, therefore, lies in the hands of his parliamentary colleagues, whenever the contest comes.

An MP who is a constitutional authority told me of his belief that even if Johnson became leader he would struggle to form a government, because a hard core of pro-Europeans might refuse to support him. Others, knowing the ambitions of their brethren, doubt that but the thought was recently echoed by the former MP Matthew Parris, probably the most articulate columnist writing in support of Cameron, who said on BBC radio that if there were a vote for Brexit he and others like him would leave the party.

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A victory for Remain might end Johnson’s prime ministerial ambitions and the prospect of such a realignment. But unless that victory is substantial – at least as large as the 55-45 vote in the Scottish referendum – Cameron will struggle: and even that margin of victory in Scotland has not squashed demands for another vote.

The Prime Minister has failed to grasp how many of his MPs are against the EU. A former cabinet minister, not known for hyperbole, told me that “more than 200” of the party’s 330 MPs would vote for Brexit in the privacy of the polling booths. The proportion of Leave activists is even higher. Some MPs still maintain that they can find hardly anyone in their shrunken constituency bases who wants to stay in.

What we are witnessing is the expression of the resentments and tribal hatreds of many years, in a party that has never recovered from the splits after Margaret Thatcher’s 1988 Bruges speech and the Maastricht arguments, or indeed from the conduct of the debate over the UK’s entry into the then EEC during the passage of the European Communities Bill in 1972.

A former minister, a pro-European, said: “Dave is going to have to bring in the people he has alienated but even then it is going to be hard for him to do more than limp on for a couple of years.” Another said the government now, with its small majority, deals with the Tory party on a “issue by issue” basis, seeking just to get over the next hurdle. Even if Cameron clears the Becher’s Brook-style fence marked “Brexit”, he may find a very deep ditch on the other side.

Simon Heffer is a columnist for the Daily and Sunday Telegraph