When Tony Blair's cabinet was going through an especially torrid patch, his aides used to joke darkly: "It has been the government's worst week since the last worst week."

The last seven days have been – in headline terms at least – the coalition's worst week full stop. As if someone had thrown a match into a box of fireworks, pyrotechnics of various colours have exploded around many different cabinet ministers. Let us take them in no particular order. Theresa May was beaten up by the Police Federation. Liam Fox wrote another of his complaining letters to the prime minister which read like they are intended to leak and then have such an unfortunate habit of doing just that. In the latest of his missives to end up on the front page of a newspaper, the defence secretary declared war on the prime minister's commitment to enshrine in law the pledge to raise the overseas aid budget.

The accusations against Chris Huhne gathered speed. He is now the focus of a formal inquiry by Essex police into the allegation, made by his estranged wife, that he asked someone else to take the penalty points for a speeding offence. On Wednesday morning, a fellow cabinet minister described the energy secretary as "in trouble". The cabinet minister offering that friendly assessment was Ken Clarke who then set off a flash mob against himself with his maladroit remarks about rape. Number 10 was already furious with the defence secretary. Now it was besides itself about the justice secretary as well.

To give himself some light relief perhaps, the prime minister went to the Commons to watch Nick Clegg present his ideas about reforming the House of Lords. As soon as Mr Cameron had slipped away, Tory MPs got to their feet to ridicule the deputy prime minister with such a high level of relish and rudeness that they had clearly forgotten that they are supposed to be members of the same government. At his private, weekly meeting with Lib Dem MPs that night, Mr Clegg included Mr Cameron in a jibe at the Tories about the health reforms when he said: "People get confused when, one day, they hear politicians declare that they love the NHS, and the next they hear people describing themselves as government advisers saying that reform is a huge opportunity for healthcare corporations to make big profits." When reporters tried to question the health secretary about what Lib Dem attacks meant for his legislation, the already battered Andrew Lansley fled into a taxi.

Vince Cable, Michael Gove, William Hague and Caroline Spelman had a relatively quiet week, but then they deserved some time off, having previously done their fair share of generating embarrassing headlines for the government.

It is at times like this when I almost feel sorry for a prime minister. Even such a seemingly insouciant character as David Cameron must want to lay down in a darkened room and wrap his throbbing head in a towel impregnated with Samantha's aromatherapy oils. He may have consoled himself with the thought that if he has to fire someone, at least there are players waiting for promotion from the subs' bench. There's always David Laws…

Scratch that. The former chief treasury secretary, who holds the modern record for the briefest-ever cabinet career, was suspended from the Commons for seven days after a quite damning judgment on his breaches of the rules on expenses which led to his resignation last May. Much as his head for figures may be admired by both Mr Cameron and Mr Clegg, the MP for Yeovil will have to serve more time in the backbench sin bin before he can be brought back into government.

All of this looked like a gift to the leader of the opposition. If he wanted to demand the resignation of a cabinet minister, Ed Miliband was spoilt for choice. As it turned out, he made the wrong call by demanding the head of Ken Clarke. Downing Street, already frightened that it has lost the Tory tabloids on law and order, was certainly cross with the justice secretary, but the prime minister was not going to fire him at the behest of the Labour party. Memo to Mr Miliband: only call for a resignation when there is a decent chance that it will actually happen.

The prime minister will want to try to work out why so many of his cabinet are deliberately making trouble or falling into the mire. There is no quickly discernible pattern to this. Theresa May is feeling the thick end of the coppers' truncheons because that is what the police always do to any home secretary who takes them on. The quietest figure among the major secretaries of state until now, this will be a big test of her resilience. In that regard, she might observe Chris Huhne whose outwardly calm demeanour is a wonder to colleagues. "He came into cabinet and carried on as if it was business as usual," says a fellow minister. "I don't know how he does it. I couldn't."

The pressure on the energy secretary has nothing to do with policy. He is generally rated in Whitehall as one of the more hard-headed and effective ministers. The alleged crime took place eight years ago, before he was even an MP, and would not be generating headlines had he not left his wife. With him, it is personal, not business.

The eruption around Ken Clarke was ignited because he spoke very clumsily on a highly sensitive subject, thus arousing against himself an unusual alliance of furious feminists, frothing tabloids, point-scoring Labour MPs and rightwing Tories who think the justice secretary is "soft" on crime. He eventually managed to calm the storm by apologising gracefully, but he prolonged the furore by being slow to explain himself. That is probably because Ken Clarke is a politician who first sat in a cabinet long before the development of the 24/7 media and has not fully adjusted to the accelerated speed of the news cycle.

At first glance, these cabinet ministers seem to have nothing in common other than getting into trouble all at once. But gaze into the swirl for a while and some patterns become apparent. One connecting theme is the consequences of the spending cuts. When the cabinet agreed their budgets last autumn, there was much marvelling that the negotiations had taken place with such apparent ease that the prime minister did not once have to convene the Star Chamber to arbitrate between the Treasury and spending departments. I wondered then whether it had been too smooth: naive, inexperienced, zealous or too-eager-to-please ministers had committed to swingeing cuts without grasping how difficult it would be to deliver them.

There was an early sign of this when Caroline Spelman came a cropper over selling woodlands; another indication when Michael Gove had to part-reverse on some of the cuts to the schools budget. Theresa May is signed up to delivering a 20% cut. Not surprising that you won't find any laughing policemen. Even those sympathetic to Ken Clarke's emphasis on reducing reoffending and increasing rehabilitation wonder how he can find the money necessary to be effective when the Department of Justice is committed to an even bigger percentage cut than that taken by the Home Office. Dr Fox is sniffing around the money marked for overseas aid because his defence budget is such a terrible mess.

A related theme is the way in which ministers have launched into contentious reforms, health being the prime example, without preparing the ground with interest groups or the public. That is making delivery a whole lot harder than some ministers glibly imagined in the early days of the coalition.As things get tougher for the government, there will be a premium on the cabinet sticking together if they are to weather the storms ahead. So the most worrying development for the prime minister is the emergence of a third theme: lack of solidarity. In its salad days, the coalition looked like a government of chums. William Hague told me that they were a much more cohesive cabinet than the purely Tory one that he sat in during John Major's time. Other cabinet members observed that the government was much more harmonious than it was when war raged between Tony Blair and Gordon Brown.

That atmosphere of unity has now dissipated. Not one Tory cabinet member turned up to show support for Chris Huhne when he had to face the Commons. Newsnight could not find a single minister to bat for Ken Clarke. The Tory whips couldn't stop – or didn't even bother trying to stop – Conservative MPs from monstering Nick Clegg. There are Tories who now refer to the Lib Dems as "yellow bastards", a feeling amply reciprocated by some of Mr Clegg's MPs. Dr Fox's leaked letters play to the rightwing gallery of the Tory party at the expense of Conservative colleagues. The government is beginning to factionalise and ministers behave as if it is every man for himself.

Tomorrow, David Cameron will make his latest speech trying to breathe life into the big society. He will exhort us to love our neighbour. It might be more appropriate to make the speech to his own cabinet.