Great Clifton is just off the A66 Cockermouth to Workington road, but closer to Workington. I've never asked anyone, but doubt that anyone from Clifton would consider themselves from Workington.
Some of the clubs mentioned, Salterbeck, Westfield etc are from in the town of Workington, but generally the long standing clubs with history, their own club houses, junior set ups etc are from the towns and villages near Workington.
I may be wrong here, but I think most of the great Cumbrian players who have played for Workington have come from Maryport area, Broughton, Seaton or come up the road from Whitehaven