This was originally a poem written by one Thomas Tusser (1524?-1580) http://en.wikipedia.org/wiki/Thomas_Tusser and included in his long poem “A Hundreth Good Pointes of Husbandrie.”  The poem was reprinted in several works in the early 19^th Century, e.g. Douce – “Illustrations of Shakespeare and of ancient manners” (1807) and Southey – “Selected Works of the British poets from Chaucer to Jonson” (1831).

The original poem is

Of Christ cometh Christmas, the name with the feast,
A time full of joy, to the greatest and least;
At Christmas was Christ, our Saviour, born,-
The world through sin altogether forlorn.

At Christmas the days do begin to take length,
Of Christ doth religion, chiefly take strength:
As Christmas is only a figure or trope,
So only in Christ is the strength of our hope.

At Christmas we banquet, the rich with the poor,
Who then, but the miser, but openeth his door?
At Christmas, of Christ many carols we sing,
And give many gifts, in the joy of that king.

At Christmas, in Christ we rejoice, and be glad,
As onely of whom our comfort is had:
At Christmas, we joy altogether with mirth,
For his sake, that joyed us all with his birth.

We can surmise that the version that Mr Gill sings derives from one of these later sources, but it is not known when the poem was put to music.

Notes by Gwilym Davies with information provided by Mick Pearce