The voice is John Tams, who is already noted as being heavily involved with the music for "Sharpe". I don't know the tune he is using, nor the exact set of words, but both seem a variant (among many) of the song Banks of the Roses. In some versions this in turn shares some lines with the Nightingales song mentioned by DtE above. Doubtless someone more scholarly than I has investigated the overlaps.

I wonder whether JT was creating something of recognizable origins, but in fact his own, as I understand he did with adding new verses to O'er the Hills. Unfortunately the end credits are missing on my recording of this episode, they might have helped.

The words sung are as follows:
I'm off to India for seven long years,
Drinking wine and strong liquor, instead of small beer,
But if ever I return again it will be all in the spring,
And we'll go roving through the banks of red roses.