I was inspired by an article at fullfacts.org to look at the success or otherwise of British Prime Ministers who become PM during a Parliament compared to those who become so by winning an election. Despite the furore raised by Britain's right wing press when Gordon Brown succeeded Tony Blair in 2007, this is a pretty common occurrence with over 40% of Britain's Prime Ministers taking over mid Parliament. Theresa May is the first to call an election asking for a personal mandate as opposed to inheriting her Party's.
I made this chart, although the chart at fullfact.org is also very descriptive. The chart below runs from 1945 as I decided to pay less attention to those premiers before 1945; Britain was a different society and universal suffrage was still qualified, at least for some of their timeline.
Election winners are represented by a solid rising bar. Inheritors are represented by a falling hatched bar, darkly hatched if they won their next election and lightly hatched in they did not. The length of the line shows how long their administrations lasted. (roughly).
I am not sure what lessons to draw. We don't know what'll happen to May, but we should note that neither she, nor Gordon Brown faced an internal competition when they succeeded their predecessors; neither faced their party membership. Having to do so gets some stuff out the way. It's hard for the Tories to throw any dirt at Jeremy Corbyn that hasn't already been thrown by opponents in his own party. Also the last successful inheritor was John Major, who fought an election, albeit only in Parliament against the finest Tories of his generation, or at least those left after 10 years of Thatcher and did so a second time to unite his party. It's possible that this suggests that strong Party mandates are important.
In my blog article, I say a bit more and note that this chart hides the contributions of those Party leaders who never got to be Prime Minister.