I wonder if we have different reference books, and my memory is playing tricks, but I am pretty sure Callaghan was an MP whilst PM.
Wikipedia confirms it although of course it isn't always reliable
Cardiff South East was a parliamentary constituency in Cardiff, Wales. It returned one Member of Parliament to the House of Commons of the Parliament of the United Kingdom.
The constituency was created for the 1950 general election, and abolished for the 1983 general election. Its only MP was Labour's James Callaghan, who served as prime minister from 1976 to 1979, while serving as the seat's MP. Its present-day equivalent is Cardiff South and Penarth.
I think you are right about Lord Home though- I am not sure why Quora doesn't include him.