Apart from Geoffrey Chaucer, elected as the MP for Kent in 1386 (whose own son Thomas sat for Oxfordshire on and off between 1401 and 1421), the only poet laureate and member of parliament was Henry Pye.
Pye sat for Berkshire (1784- 90) and took up the laureateship after William Hayley turned it down on Thomas Warton’s death. He is often cited as the worst laureate ever, but he had at least one fan, in the Commons – William Mitford, the Tory MP for Newport, Bere Alston and New Romney intermittently between 1785 and 1818. Pye dedicated a sonnet to him:
. . . Nor will you, though your
nicer ear retain
What sounds to purest
This tribute from a ruder
Proud to record your friendship
in his song.