Through the kind offices of the author, I have managed to get hold of an off-print of:
Clay drainage and pipe manufacture at Johnby Whythes, Greystoke, c.1851-1909 by E Davis
Transactions of the Cumberland & Westomorland Antiquarian & Archaeological Society, Volume II, 2002, 261-275
It is a study of that tile works (including quantities produced and ownership), and also comments on the types of drainage tiles available in Cumberland. A great addition to my library!
February 2014: E Davis, along with S B Davis, have also published their work about Cumbrian drainage as a whole, and details can be found here: http://bleatings.blogspot.co.uk/2014/02/book-draining-cumbrian-landscape-by.html