Where do my connections to the name Jenkinson go back to?

For as long as I can remember there has always been the joke that my father, Walter, was Walter Jenkinson the third, and now I know the reason why.
Born in 1937 to Walter and Ellen Jenkinson (Reed Moss) there goes the first reason out of the bag. My father Walter was named after his father Walter.
My grandfather was Walter Jenkinson, born 11 November 1909 at 5 Court Hoyle Street, Sheffield. By December 1936 he had met and married my grandmother Ellen Reed Moss the third child of George and Annie Reed (Moss). After setting home in the Penistone Road area they were to have only one child, my father, during the time of the Second World War.
My grandfather worked as a labourer for most of his life in the Penistone Road area. Eventually my grandparents were to settle not far from there and this is where my grandmother still lives, age 90 years.
And here now lies the second reason as to why the reason why my father is Walter Jenkinson III.
Walter Jenkinson born 1909 was the son of, yes you've guessed it, Walter and Ellen Jenkinson (Knight) Walter Jenkinson (the first) was born sometime around 1887/1888 and appears on the 1881 census as living on Lambert Street in Sheffield. At this time he was aged 3. His parents were Charles and Annie Jenkinson who appear on the 1861 census as living on Neepsend Lane at no 51.
There is reason to believe (thanks to the research done by Karen Lightowler) that a man by the name of Jenkinson died in the Sheffield Flood in 1864, however a relationship to this family at this time cannot be proven as no records show of a death of a Jenkinson, however other documents relate to this chap, and his death.
Charles Jenkinson was born 1853 and was the son of Oliver and Mary Ann Jenkinson (?). Oliver was from Leeds, as was his wife. There is reason to believe that Oliver was the son of John and Elizabeth Jenkinson (Oliver). I have records of a birth in 1814 of a Oliver Jenkinson to a John and Elizabeth Jenkinson. This also relates to the marriage of a John Jenkinson to an Elizabeth Oliver. I am assuming here that Oliver was given his mothers maiden name as a first name.
Coming forward then in time John and Elizabeth had three known children, Oliver, Mary and Iddo. I know nothing other than the christening date of Mary, however I have more information on Iddo born 1822 and his family. Iddo met and married a lady by the name of Emily Wormold who was born 1822 in London Middlesex. The two had, to my knowledge, a total of nine children.
George born 1845, Frank 1848, Arthur Brown 1849, Irwin 1851, Elizabeth 1854, Rachel 1855, Emma 1858, Charles Iddo 1860 and and Ada 1865.
Charles Iddo born 1860 went on to marry Martha Creswell and they had amonst others, a son, Charles Iddo Jenkinson born 1885. It is this Charles Iddo that went onto form CI Jenkinson and Sons, Tool Manufacturers. Later to become NILOC Tools in Sheffield.
Again I have more information and what I have given is only but a brief outline. Please contact me direct for further information.