In traditional fashion, most of the fell packs in Cumbria have similar songs to this, but while each will use the same tune they'll all have different words, referring to personnel and places familiar to their own hunt, eg Walla Crag - a song of the Blencathra Hunt, which starts:
Twas early one morn at the break of the day
Jim Dalton the Huntsman, he hastened away
To Walla Crag where he uncoupled his hounds
The woods and the valleys did music resound.
Chorus:   Tally -ho! Hark Away! Tally-ho! Hark away!
            Tally-ho! Tally-ho! Hark away!
(and on for 12 more verses!)

Or Cartmel Hunting Song 1924 (songs often mark one particular, special hunt that has entered the hunt folklore)- or The Unicorn Hunt, Ambleside (NO ... the Unicorn is the name of the pub: they will still hunting foxes!)

Then there's The Welton Hunt, sung by Joe Thompson on 'Pass the Jug Round' (Veteran VT142CD)- archive recording of c. 1953 which has same tune, and chorus 'Hark for'ard away, Hark for'ard away
            Altogether good hounds hark away'

There's always been a constant re-making. One of my favourite more recent songs, from the Cumberland Farmers Hunt, is The Hound Pup - to the tune of 'Seasons in the Sun.'