"(Molly/Polly/Kitty) put the kettle on, Sally blow the dinner horn... We'll all take tea." Often a fiddle tune with the usual sorts of verses for a fiddle tune
Opie-Oxford2 re 420: "Around 1810 the song was clearly the rage in London."
The following broadside refers to the original song and quotes it as a chorus.
Bodleian, Harding B 11(4332), "Polly Put the Kettle On" ("I am a merry, happy chap"), C. Sheard (London), 1840-1866 - BS
According to Eric Partridge's _A Dictionary of Slang and Unconventional English_ (combined fifth edition with dictionary and supplement, Macmillan, 1961), this was a c[atch] p[hrase] from around 1870, since become obsolescent. He attributes it to "the song of Grip, the Raven (Dickens)." Since Dickens was born 1812, the poem would appear to precede him, but he may well have added to its popularity.
The book involved, _Barnaby Rudge_, is based on the anti-Catholic riot of June 1780, but is influenced, e.g., by Sir Walter Scott, so there is no particular reason to think the catch-phrase dates from that era.
Grip is the mentally defiient Barnaby's pet raven, given to phrases such as "I'm a devil," "Never say die," and "Polly, put the kettle on." The latter quote occurs in chapter 17. - RBW