The British Prime Minister with the total shortest period in office (barring a few caretakers or people who never really took office) was George Canning, whose sole term lasted 119 days from 12 April 1827 until his death on 8 August 1827. In order not to become the new holder of this somewhat ignominious record, Boris de Pfeffel Johnson would have to still be in office by Wednesday 20 November. I don't think he's going to make it, do you?