Thanks for all your help Rokerman and Pauline,
I took time to reply because I have pieced together a theory from the information so kindly given which I wished to share, with all its gaps and fancies.
The name Euphemia is relatively rare and therefore a good tracking clue, and the ages throughout match to within a year or could have easily been switched between siblings by the census recorder. So here goes!
Eupehmia Morris ( surname from family folklore!) b. 1817 Lilburn in Eglingham Parish Nrthbld, marries ( date unknown) Thomas Cook b. 1808 agricultural labourer from Bambraugh (known as Bambrough, now Bamburgh, just north of Eglingham. Thomas also is a name which is mentioned in our family folklore.
Daughter Jane is born 1838 in Bambraugh.
Family Cook moves to Newcastle on Tyne ( to seek their fortune/work?) where daughter Margaret (1846) and sons John (1840) , Charlton (1847), and Thomas (1850) are born. ( The census recorder cannot spell Euphemia!)
A tragedy happens between 1851 and 1861. Could that have been the Newcastle Cholera Epidemic of 1854? John and Jane could have been of an age to have married and / or moved on, but there is no record of Margaret, Charleton and Thomas Jnr in the 1861 census. I will have to look for a number of death certificates.
Between 1851 and 1861, Euphemia and Thomas Snr move from the city to Wylam in the Parish of Ovington , Nrthbld on the Durham border west of Newcastle ( where Thomas Snr either worked as a miner or as a labourer at Holeyn Hall , later home of Sir Charles Parsons, inventor of the first multi stage steam engine- Holeyn Hall if spoken in rapid Geordie dialect could be taken by an 1881 census recorder especially if rendered by an aging Euphemia as "halliwell" - and moving to Wylam could have been a tonic to a berieved family. All in these brackets is my speculation to be proved or otherwise!)
Sons Joseph (1852) and James (1855) are born at Wylam.
The Cook family moved between 1855 and 1858 further north to Lynmouth ( Linmouth ) , a coastal town in the Woodhorn Parish where son Robert was born (1858) and where, presumably, Thomas Snr worked as a miner.
Between 1858 and !861, Thomas Snr must have died and widowed Euphemia and her three sons set up a shop ( type unknown) in Monkseaton Village adjacent to Cullercoates near Tynemouth.
By 1881, son James Cook had married (date unknown) Ellen (b. 1851) of Chatton, Nthbld and is a coal miner at North Seaton colliery, living at North Seaton Low Quay, Nrthbld with his new daughter Emily (b. 1880 , North Seaton).
Son Joseph Cook is a batchelor coal miner at North Seaton colliery , living at North Seaton Low Quay, Nrthbld, with his aging widowed mother Eupehmia (now 64 years old).
Presumably, son Robert Cook has died or moved away because I cannot find a 23 year old Robert Cook in this region in the 1881 census.
Eventually, (date unknown) , Joseph Cook ( my great grandfather) marries Elizabeth ( Rutherford) Wheatley (b.1858/59) Cambois, Nrthbld and the Wheatley's are another story ( including the ferrymen of the Wansbeck at Cambois) on which I have some info and will follow up later!
What happened to the Cook's from 1881 through the 1900's ( or for that matter prior to 1800) are also other stories, except my grandfather is Josiah Wheatley Cook, a miner at North Seaton colliery who married Eliza Hannah Coggins and eventually lived and died in Newbiggin-by- sea. One other name crops up in my early reseach as a Wheatley nephew - Frederick Greenshields( b 1874 Essex London) whose mother was born in Newbiggin-by sea in 1809 and living in Newbiggin- by -sea in 1881. The tie in remains a mystery.
If any Rootschatters with Cook/Wheatley/Rutherford/Morris /Greenshields
roots in these parts of Northumberland can help or use this story or if I seem way off base in any part please let me know. I have my work cut out for me now to prove it!
Thanks for the help and reading!
Lumber-Jack