The main line of Starkeys/Starkies/Starkys originate in Stretton, Cheshire in the 13th Century, information derived from Omerod's History of Cheshire which shows printed pedigrees generated from Herald's Visitations of Cheshire. There are several lines descended from there. There is a family coat of arms featuring one, three or 6 storks depending on which line the arms belong to.
If you have a map of the UK look for the crossing of the M62 and M6 motorways then check the South East quadrant of the intersection for Stretton.
Several Starkeys were Sherrifs of Lancaster and their coats of arms are on display in the Shire Hall in Lancaster castle.
I have a pedigree of these Starkeys if you are interested. E-mail is firstname.lastname@example.org