How many shambles add up to omni, how many balls-ups do we need before calling it a disaster, how many U-turns does it take to make a failed government? Not a week or even a day seems to pass without another crisis afflicting the coalition government, or more evidence of a cabinet divided within itself, and with a rare capacity for self-inflicted wounds.

Sunday's news that the cabinet are at sixes and sevens over policy towards China, with David Cameron and George Osborne in favour of a conciliatory response to Chinese provocations and William Hague and Nick Clegg urging defiance, is merely a characteristic example. The cynical Lord Melbourne, Queen Victoria's first prime minister, liked to tell his cabinet ministers: "It is not much matter which we say, but mind, we must all say the same." That sensible maxim was forgotten as soon as the coalition was formed.

That came at the end of a week that had seen Michael Gove's embarrassing retreat on GCSEs and the legal ruling against welfare-to-work. Any government has setbacks and is obliged to deal with unforeseen events, but this government too often gives the impression that it simply doesn't know what it's doing, while it has been distinguished by sheer ineptitude and own goals.

Three years ago most British voters thought that we needed a new government, if only to replace what had aptly been called the tawdriest regime in postwar British history. When the coalition was formed it enjoyed much goodwill. It was, after all, the first British multiparty government of my lifetime, the first that included a party called Liberal, and the first whose MPs had been elected by a majority of votes cast (59% if you add Tory and Lib-Dem votes, something of an improvement on the 35% of the vote with which Labour "won" in 2005).

Clearly, there were grave problems ahead with the economy as it was. But that does not account for the catalogue of unforced errors. As must be now painfully clear to Cameron, setting up the Leveson inquiry was one of them, a panic-stricken response to a scandal that was painfully close to Cameron himself. Apart from the further humiliations it produced for a prime minister who didn't know that "LOL" meant "laugh out loud", he is now stuck with Leveson's report. He had already managed to unite the Guardian and the Daily Mail in their contempt for him. Now he finds himself in a hopeless bind, since whatever his response to Leveson, implementing the recommendations in full, not all or somewhere in between, he is on a hiding to nothing and can only incur further obloquy.

But of all Cameron's own goals, none is stranger than the same-sex marriage bill. Try to set aside the rights and wrongs and look at this in terms of brute calculation of political advantage (and that's how politicians do view matters, whatever they may say to the contrary). Bear in mind that Cameron's critics are correct when they say that same-sex marriage was in neither the Tory manifesto (or any other party's) or the coalition agreement.

To make this clearer, go back 45 or more years, as some of us can, to the famous liberal reforms passed by parliament under Harold Wilson's government in the late 1960s, on abortion, homosexuality and divorce. I am old enough not only to remember them but to have collected signatures when I was an undergraduate on a petition for the repeal of the existing law criminalising homosexuality, one of my last political activities and for all I know my only good deed.

But although the bills were passed under the Wilson government, they were not introduced by it. They were all private members' bills. Abortion reform was sponsored by a recently elected Liberal called David Steel, and homosexual decriminalisation by Leo Abse, an eccentric Labour MP (and by another eccentric who deserves to be remembered with honour, "Boofy" the Earl of Arran, a Wodehousian peer who bravely steered the bill through the Lords).

As a result, although the measures were contentious, there was no animosity between parties – or within them, a contrast indeed with this latest episode. So why did Cameron bring in the bill? The answer given by his somewhat diminished claque of sycophantic admirers in the media is that it was part of his mission to detoxify the Conservatives and show they aren't the "nasty party" any more. In that case he conspicuously failed in his own terms, since more Tory MPs voted against the bill than for it. He has merely reminded us that he is the weak leader of a bitterly divided party.

But in any case, with his PR man's belief that presentation and image are all that matters, Cameron has never understood that the Tories aren't supposed to be nice. Conservatives are there to expose progressive humbug and the follies of the age (or if you prefer, as one American liberal put it, the purpose of conservatism is to keep liberals honest). The Tories aren't meant to be the nice party, they are meant to be the competent party, and if they cease to be that there is no hope for them.

Maybe the most chilling news of all for No 10 this weekend was a poll ranking the eight premiers of the past 50 years. Cameron came fifth, ahead only of John Major and Gordon Brown. The clear winner, 23 points ahead of Cameron, is Margaret Thatcher, and rightly so, in my view, on the simple ground that she and Attlee are the only two prime ministers since the war who changed the country and changed the political landscape.

Did people vote for Thatcher – 13.8 million of them, don't forget, in 1987, as against 9.5 million who voted for Blair in 2005 or 10.7 million who voted for Cameron three years ago – because she was nice? I think not. People didn't like Thatcher, they respected her.

Cameron, who once wanted to be "Blair's heir", evinces all of Blair's lack of principle with none of the guile. Sadder still, a man desperate to be loved is widely disliked and, even worse, just plain dissed.