http://www.bbc.co.uk/kent/voices/hartlake/hop_picking.shtmlSee this interesting BBC link re gypsy itinerant agricultural workers in the 19th century. Although this refers to Romany gypsies, I think the Corks/Cooleys weren't true Romanies, but merely travellers.
In the history I've found, within the family were hawkers, general dealers, marine store dealers, chair bottomers etc., and Richard Corke (1812, Stone, Kent) seemed to carry out agricultural work, following the requirements of the farming year.
He carried on until he was nearly 80, finally dying of burns when he set fire to himself whilst sleeping (with the farmer's agreement) in a barn, probably during the hop harvest. I've seen where he died, in Otford, Kent, a small town where what struck me most was the number of pubs. I hope that he had a convivial evening, after a hard day's work, and didn't know much about what happened.
In terms of Nathan Evenden and the reference to previously living in Barking, Essex, I wonder if he had travelled in work - after all, the family in 1891 is in Woolwich (on the South side of the Thames, but otherwise not very far away from Barking on the Essex side of the river).
And I expect the family were living in the Hop Barn whilst Nathan was working on the farm. Thomas Duddy apparently was a landowner in Hunton, and although I can't see the farm now, it's not a very large place and therefore you can see country very like where your grandmother was born from google earth.