Wainwright describes the fell as functional rather than ornamental, writing: "Viewed from a distance Great Cockup appears as a modest but extensive eminence with no obvious summit and nothing calling for closer inspection.

[2] The prefix "great" distinguishes the fell from its smaller neighbour Little Cockup, which lies on its north-western shoulder overlooking the hamlet of Orthwaite, with a height of 395 metres (1,296 ft).

The word "cockup" denotes a blunder in colloquial English; this prompted Denis Norden to visit the fell in an edition of It'll be Alright on the Night, a programme featuring outtakes from film and television.

The fell has a series of stone-built grouse butts 500 metres (1,600 ft) west of the summit, some of which have been dismantled leaving just the foundations in the ground; they can confuse walkers as to their original purpose.

[3] On 21 December 2020, YouTuber Tom Scott posted a video where he hiked Great Cockup whilst he gave a monologue to camera, in homage to the aforementioned TV show's title sequence which took place on the hill.