Mike - the K14 and K15 did not have gangways fitted, although the K15 had 'psuedo' corridor panelling on the ends, so in theory could have been fitted with gangways at a later date. The K16s were fitted with gangways from new.
Ah ha! You may have stumbled on the key to the OP's question, namely that, in later years, brake vehicles without a lockable guards compartment would qualify only as a 'Van'.