That text is copied from Bramley & Stainer, so I didn't mention it. I ought to have done, though, as the links to various forms of This Endris Night are interesting and relevant, and an early tune is reproduced from Shaw and Dearmer's English Carol Book.

Bramley and Stainer list their melody as written by the organist and composer Charles Steggall (1826-1905).

Assuming that this (in one or other of its forms) is the song wanted, it's likely enough that "Taunton Carol" is just a local name; much as other carols and songs have acquired local names while originating elsewhere (Holmfirth Anthem, for example).