There is no correlation between a/a collars and cap badges. Collars were often sealed and made in a/a long before cap badges as stocks of collars were often smaller, and thus used up faster, than cap badges. Same goes for a/a buttons.
Quite right Alan. To correlate collars with badges is quite foolish and if one reads Army Dress Committee minutes one will find that seldom (if ever) are the two authorised at the same time.