I would say that, by a process of elimination, John Beck, shipwright, has to be your No. 1 candidate.
The only other John Beck in Newcastle at this time is John Beck, grocer (c1790-1830), who can be almost ruled out because his first wife, Mary Lowes, who he m. by banns at St. John on 11 Oct 1819, died in September 1820 (buried on the 29th at St. Nicholas) ... the same year that he was declared a bankrupt ... and he only looks to have had one child by his 2nd wife Elizabeth Talentyre (m. 22 May 1824 at St. John) - Jacob Wilson Beck (x 3 Apr 1825 at St. John).
This John Beck died c. 1 Jan 1830 and was buried 3rd Jan 1830 (from St. Nicholas parish) at St. Andrew. His widow re-married to Thomas Mowbray the following year and received a nice inheritance from her half-brother John Bulman Armstrong in 1834. Son Jacob Beck can be seen in the 1851 census with his half-brother Thomas Mowbray.
So it seems very unlikely that your John Beck hails from that lot. As for the intriguing Ann Gleghorn, she is described as 'servant', and perhaps that is all the relationship was although it's unusual at that date for a servant to have followed her master from Westoe to Cowpen. Perhaps she was a sort of nanny to John - he's very young in 1841 - as it's not often you come across coal miners with domestic servants. I think she's probably the Ann Leaming/Leeman/Lemon who married Thomas Gleghorn at Earsdon in 1795 and who died 11 Oct 1857 at Blyth ("At Blyth, 11th inst., aged 89, Ann, widow of Mr. Thos Gleghorn, tailor." [Morpeth Herald, 17 Oct 1857]. Maybe there's a clue in there somewhere ... hope so.