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Hello Garstonite  Yes, I did look into that but research says that men who were called up were between 18-41.  Of course, we know that not to be true as young men were often not as old as 18.
I did find this record: Archibald Middleton aboard the Indefatigable died 31st May 1916 but really can't be sure it's the right Archibald

I'm trying to find the whereabouts of Archibald Middleton b1871 Durham
He has a son by an Elizabeth Chamberlain b1876, Archibald McKinley Middleton b 3rd June 1900 Christchurch, Burton on Trent.  !901 Archibald Jnr and mother are at her parents home in Burton on Trent   In 1911 Archibald is still living with his grandparents.  Possibly his mother is a servant to a bank manager in Burton.  Possibles for Archibald senior:  1901 a visitor to a house in Fulham, occ engineer (consistent with occ on son's birth certificate) 1911 Census boarder in a household in Willesden, London Occ engineer.  On his son's marriage in March 1926, he is listed as deceased.  I can find no record of his birth, death or marriage.
Any help would be much appreciated. 

Hello Carole
EDIT:  I 've found something which doesn't ring true, unless I've totally lost the plot!
As I said, I followed up the other children.
1901 Census Samuel and John are living in Derbyshire- 146 Primrose Hill - same date of birth and place of birth.  It seems that they may have changed their name from Cotton to Roberts.  Their mother's maiden name.  It could be that she was never married to William Cotton.  Of course, this could be totally wrong.
Moving on to Joseph, who is my main focus, thanks I'll check that.

Hello
I'm having trouble finding a Joseph Smith born on 1st November 1890 in Hanley, Staffs
Parents: Thomas Smith b1849 and Annie Marie Roberts b1859. (married 1882)
Siblings: Samuel Cotton step-brother b1878 and John Cotton step-brother b1884
Siblings:  Elizabeth Smith b.1887 and Ann M Smith b1888
1891 Census shows the family living in Hanley, Staffs.
I can find Joseph on no other Census, marriage, death or military.     Thank you

Many thanks for your replies.  They've been very helpful