So in another most entertaining twist in British politics - and I remember the spasm that ejected Mrs Thatcher; this is even more baroque - Liz Truss is resigning. This time it'll supposedly take only a week to name a successor - if they can find one! - which will leave her at less than two months in office.
To my mind Truss's reign will be summed up by Commons leader Penny Mordaunt stating, in a debate, that "The Prime Minister is not under a desk."
(This was in response to an opposition MP claiming that she was cowering in fear of making decisions, and asking that they get someone else instead. Well now they will.)
Depending on criteria that may be the shortest term as PM ever. George Canning died after 4 months in 1827, but the most elaborate succession crisis in British history was 1834-35, when King William IV fired the Whig government of Lord Melbourne - the last time a monarch tried such a move - and put in the Tories. The Duke of Wellington, the previous Tory leader, insisted he had retired, and had passed the torch to Robert Peel. But Peel, with uncharacteristic bad judgment, had chosen this time to vacation in Italy, and in pre-railroad pre-telegraph days it took 3 weeks to fetch him back, during which time Wellington acted as interim caretaker. If that counts, that's a shorter term. (Wellington had been PM before, for just under 3 years.)
But the Commons was still dominated by the Whigs, so Peel gave up after four months - just a day or two more than Canning's term - and the Whigs came back in. The gradual crystallization of the party system out of the amorphous masses it had been in the 18C is what made the selection of a government a matter of nose-counting and no longer monarchial selection.
Although that was still always tempered by whether Parliament will accept them, which is why the real shortest Prime Ministership - so short it's not always included in the lists - was that of William Earl of Bath in 1746. He formally accepted office but found that gaining support was futile, and gave up after two days.