This has to be the definitive version. It is from "Songs Of Northern England" By John Stokoe, published in 1893. It is considered to be the extended version of the "Northumbrian Minstrelsy".

I Cannot get to my love, if I would dee,
The water of Tyne runs between him and me,
And here I must stand with a tear in my e'ee,
Both sighing and sickly my sweetheart to see.

O where is the boatman? my bonny hinny!
O where is the boatman? bring him to me,
To ferry me over the Tyne to my honey,
and I will remember the boatman and thee.

O bring me a boatman, I'll give any money,
and you for your trouble rewarded shall be,
To ferry me over the Tyne to my honey,
Or scull him across that rough river to me.

Stokoe says in his notes on the song that "The version of the ballad is from John Bell's "Rhymes of The Northern Bards", 1812. The tune is common in Tynedale and Redesdale, and,like many other beautiful old airs, has been seized upon and used by "patterers" and "street singers" until it has nearly passed with their lugubriously pathetic productions into oblivion".

Of course I'm sure that no one in Ian McCullock's company at Durham City Folk Club could be accused of that but I'm sure no one would object if you were to sing hinny instead of honey, as seems to be the usual way people sing it currently.