I would recommend purchasing the 1917 marriage certificate, which will give you Joseph and Annie's ages, father's names, occupations, etc. Hopefully then we can identify them in earlier records. (There seem to be a number of marriages for Joseph Kosky, so hard to say if the 1897 birth is him).
http://www.gazettes-online.co.uk/ shows Arthur's name change, dated 8th April 1942 - Arthur Stanley Kaye, of "The Lodge", Marlow Road, East Ham, Essex, a natural born British subject, renounced and abandoned the name Kosky and assumed in lieu thereof the surname Kaye.
Interestingly enough, he does not appear to have been the only one to make the Kosky -> Kaye change.