Your not missing much, it closed in about 1982 because an internal wall had cracked and it was flooding badly. It's flooded within inches of the hatch if i remember rightly.
Post Organisation of York Group (45 Cluster ) Schedule of Posts 1980
45 M CAMBLESFORTH SE64892647
46 CAWOOD SE58053894
47 FULFORD (II) SE61784980
1989 Schedule of Posts
45 M CAMBLESFORTH SE64892647
46 BARKSTON ASH
47 FULFORD (II) SE61784980
1991 Schedule of Posts
45 M CAMBLESFORTH SE64892647
46 BARKSTON ASH NOT IN SERVICE
47 FULFORD (II) SE61784980
It appears after Cawood closed in 1982, it was replaced for approximatly five years by Barkston Ash (which priveiously closed in 1968). However it is clear from the 1991 Shedule of Posts that it had closed so i can only presume it was removed in the final re-organisations of 1989