Thansk for your message. I do not think there is a close direct connection between your father and the family of William John Leadbeater. He was the son of Alexander Francis leadbeater and Ellen Elbe who were married in St Pancras on 5th April 1874. They had at least the following children. Alexander Francis born 1875, Harriet Ellen born 1877 and William John born 1882.
Alexander Francis was born on 30th May 1840 and his parents were Alexander Leadbeater and Mary Anne Kelsey who were married in October 1839 at the Parish Chuech in Paddington.
William John Married Ethel Beatrice Clark and had at least the following children. William Robert 1918, Stanley 1924.