David Laws's resignation after only 17 days in the Cabinet has prompted quite a few people on Twitter to ask if he was the shortest ever Cabinet Minister. And this is the sort of challenge I can't refuse, especially as some have specifically asked me... My instinctive response is "No" but I've had to look this up a bit. A few examples follow:
My first instinct was the "Short Lived Ministry" begun on February 10th 1746 by the Earl of Bath. This ministry usually doesn't appear in the history books and some make the case that it doesn't even count. What happened was that the existing "Prime Minister" (the title wasn't official in those days) Henry Pelham and George II fell out and so the King turned to Bath to see if he could form an alternative ministry. Bath gave up after two days, after only he and Lord Carteret had "kissed hands" and taken seals as First Lord of the Treasury and Secretary of State for both the Northern & Southern Departments respectively. But quite apart from whether or not this ministry actually counts at all, both had held Cabinet posts before.
Lord Frederick Cavendish was appointed Chief Secretary for Ireland in May 1882. He formally took the oath on May 6th at Dublin Castle. That afternoon he was murdered along with Thomas Henry Burke, the Permanent Under Secretary at the Irish Office, in Phoenix Park. But he was not a Cabinet Minister.
Earl Temple who served for only four days as both Home Secretary and Foreign Secretary. Temple was appointed on December 19th 1783 when William Pitt the Younger formed his first ministry, but resigned two days later with his successors appointed after another couple of days. Historians disagree as to the reasons for his resignation - William Hague, in his biography of Pitt, suggests that it was for a multitude of reasons stemming from the entire political situation in which George III had dismissed the Fox-North Coalition after its flagship proposed legislation, the East India Bill, had failed in the Lords because the King himself had informed the Lords he would regard any peer who voted for the legislation as his enemy. The message was delivered by Temple.
I'm going to go with Temple as the shortest I can find. Whether he should be counted as a two or four day minister, he was certainly in the Cabinet and as far as I am aware he never otherwise served in the Cabinet (he was Lord Lieutenant of Ireland 1782-1783 and 1787-1789 but according to the relevant volume of the Oxford History of England he does not appear to have been in the Cabinet at either time).