Like Lilliburlero, Derry Down and a few others this tune has been used for many songs, this one since at least the time of George I. The original name of the tune was 'The Country Garden' as employed in the ballad operas c1730. 'The Vicar of Bray' in the song refers to the time of James I right through to George I, but in fact Simon Aleyn, the Vicar of Bray' referred to was the one who constantly switched religion in order to survive from the reign of Henry VIII to Elizabeth. (Chappell).

'Doctor Mack or Tally-ho the Hounds, Sir' seems to date from about 1800 as it appeared on broadsides at that time and then in anthologies like The Universal Songster. As you would expect the name Dr Mack is often localised to some other huntsman or generalised as in the version given above.

You can easily find the tune to Vicar of Bray by Googling if it isn't in the DT.