I found it in Dickens's magazine 'Household Words' for September 18th 1855. He relates a couple of disastrous Christmas Dinner stories from his youth. 'Disaster number one, took place in the city of Paris full twenty years ago' (making it 1835) After a lengthy intro describing his trials as an English youth in a French boarding school he moves on to one saving grace which is he spent Christmas with an English pharmacist, Batten, who had a chemist's shop in Paris. To cut a long story short Batten had an Irish cook called Mary who was rather lively, prone to tantrums and drunkenness. On Christmas Day Dickens describes her as drumming with a ladel on a pan in her drunken state and yelling out the choruses of 2 songs, viz.

Flare up, Mary! Flare up, Mary!
Fiddle iddle um tum
Tow row, row!

This very likely belongs to one of the many traditional offshoots of Dicky of Taunton Dean.

Hee roar, up she rouses,
What shall we do with the drunken sailor?

There is no indication that it has anything to do with chanteying, but it is certainly part of the chantey that has come down to us. Now if Dickens was using poetic licence to tie this up to the drunken state of the cook, it still gives us a definite date of 1865 if not 1835.