Harry Rawson worked for the Midland Railway, starting work at Derby on 15 Dec 1882. His employment records, and the 1939 Register, consistently give his date of birth as 14 Dec 1867.
In 1891 he is married to Hannah Mary Jane Carter (in 1887) and is living with her parents in Derby (RG12/2727 fol62 p5). Place of birth is Bedworth, Warwickshire. The marriage was at the Wesleyan Methodist Chapel, London Rd, Derby, and he called himself Henry. He isn't family, so I have not bought the certificate yet.
In 1901 he is with his wife and son Thomas Gregory Rawson in Derby, and gives place of birth as Exhall, Nuneaton (RG13/3219 fol118 p27).
In 1911 he has moved to Borrowash, and gives his place of birth as Exhall, Bedworth.
Some of his employment records refer to Rawson, H.S.
I reckon I have found him in 1871, as Henry Rawson, in Exhall (RG10/3172 fol96 p9):
Thomas Rawson, Head, Mar, 39, Underviewer of mines, Oxfordshire Wodewright?
Sarah Rawson, Wife, Mar, 40, , Warwickshire Bedworth
Ada Rawson, daur, , 13, Domestic servant, Derbyshire Ilkeston
Ellen Rawson, daur, 11, Scholar, Derbyshire Ilkeston
Zetiller Rawson, daur, 9, Scholar, Warwickshire Exhall
Clara Rawson, daur, 7, Scholar, Warwickshire Exhall
Sarah A Rawson, daur, 4, Scholar, Warwickshire Exhall
Henry Rawson, son, 3, Scholar, Warwickshire Exhall
But I'm having trouble locating any of the family in 1861 or 1881. I'm also have trouble finding sensible birth registrations for the children, especially Harry. There's a Clara Elizabeth Rollason was registered Q3 of 1863 in Foleshill, mother's maiden name Horton, but it looks like that couple also had a son David in Q3 of 1868 (mmn Orton), which seems too close to Harry's claimed birth.
Can anyone come up with any more clues?