Find Ancestors

I am trying to trace my grandmother she gave birth to my mother in 1909 in secret as she was in service in a big london hose she was either a ladies maid or a housekeeper on my mothers birth certificate she is down as agnes booth (formaly kirk) my mother was bought up by a family in paddington the father of my mother was a soldier at regents park barracks and his name was George Graham I think that when she gave birth she was aprox28-35 years old she might have had tree brothers 2 died as soldiers in the 1st world war

I am looking for the descendents of Henry Kirk, born Nettleham Lincs in 1847 and his second wife Clara B Gooding, born 1870 in Cheetwood, Lancashire. They married in Bedford in 1889 and had at least 2 children, Sidney, born in 1892 and Louisa Jane born in 1894. Henry has a large number of descendents through his eldest son Fred (born 1871 in Lincoln) from his first marriage to Louisa Jane Falks and none of us know anything about his second family. Additionally, I would like to trace the descendents of Henry and Louisa Jane's second son, Percy Kirk, also born in Lincoln in 1873. He married Mary Ann Stanmore in Bedford in 1894 and had a number of children, Harry who was killed in WW1 and had no offspring according to the Commonwealth War Graves Commission, Percy Bertram born 1896, Gladys Elsie born 1898 and I think also a Dorothy Louisa born 1902, Winifred May born 1904 and Alfred Henry born 1908. Both Henry and Percy and their respective families lived in close proximity to one another in Bedford and can be traced in the 1901 census. After that date the trail goes cold. Can anyone help please?