Hi - I'm a great granddaughter of William Oswald Story also of Bingfield - I think Robert was William Oswald's brother? If so that makes us fourth cousins! I am in Canada - are you in NZ or Australia?
I have done a lot of research on this family line and have not found any link to Mary Queen of Scots, unfortunately. I have, however, found direct links to other aristocratic families, including the Boleyns (Mary Boleyn - which could make us descendants of King Henry VIII - if you believe that he fathered Mary's children) as well as the Spencer family - Princes William and Harry are my 9th cousins (and likely yours too). I do have a direct link to the Stuart dynasty through the wife of William Oswald Story - Olave Janet Baldwin (Buchanan family of Dunedin/Christchurch area (Chingfield) NZ) who is 22 generations descended from the Stuarts.