Charles Dibdin jr (whom, for disambiguation, I'll refer to as Mungo, his full name being Charles Isaac Mungo Dibdin) edited a book of his father's songs--a bit odd, since they seem not to have had much contact; the father abandoned that mistress, Mungo's mother, quite early in Mungo's life and left them in destitution; he even resented Mungo's use of his patronymic.

But where there's a buck to be made, or coattails to be ridden.... Some editions of this songbook are augmented with a selection of songs by the sons Thomas and Mungo as well, which does confuse things a bit, though one augmented edition (available at Google Books) clearly identifies who wrote what. The songs with musical scores are, if I recall, all works of the father. "Click Clack" is in none of the editions.

Mungo's book of verse, Mirth and Metre, was compiled early in his songwriting career, so it doesn't contain many of his best-known songs. Notably lacking are two songs recently being discussed: "Hot Codlins" and "Typitywichet", songs which Dibdin wrote for the clown Grimaldi. "Hot Codlins" had been written a year or two previous, but "Typitywichet" wasn't even a twitch in Mungo's neurons at the time. This is the only book I know of entirely of Mungo's verse and songs; as a songwriter, he is considered light fare and a pale reflection of his father--though thankfully of a more comic, less operatic bent.