I. Charlton is mentioned a lot in Kelly's letters (often as "I.C." or "I.Ch.", once as "old Isaac"). The most likely candidate I can find on FamilySearch is Isaac Charlton, b. Apr–Jun 1838 York, d. 4 Oct 1924 Myton-on-Swale, Yorkshire. The 1901 Census shows him as living at Altofts, a place Kelly refers to in connection with him several times.

Found this based on Michael's research: 
Isaac Charlton - 1838 ~ 4th October 1924
Father: Michael Charlton - 17th January 1800 ~ 16th June 1881
Mother: Jane Cox - c1801 ~ 6th May 1878
Wife: Mary Ann Smedley - 1838 ~ 1923
Children:
   Laura Frances Houseman - 22nd Feb. 1864 ~ 28th Jan. 1960
   Phoebe Jane - 4th Dec. 1865 ~ 13th July 1951
   Stephen Jacob - April 1868 ~ April 1878
Siblings:
   Maria Charlotte Drury - 1822 ~ 15th July 1887
   Frances Ann - 15th February 1824 ~ 1835
   Caroline Emily - 3rd April 1826 ~ Oct. 1827
   Henry Charles - 29th Dec. 1827 ~ April 1899
   George (J. Kirk) - 23rd Oct. 1829 ~ 6th Aug. 1892
   Isaac - 8th February 1832 ~ September 1835
   Emily - 15th November 1833 ~ September 1835
   David (M.A. Hanson) - 21st June 1835 ~ 11th Feb. 1904
   Jacob (H. Lamb) - 3rd Dec. 1840 ~ 5th Nov. 1904
   Frances Bell - c1844 ~ 28th Dec. 1919