I'm going from memory here, right back into the 70s, but I believe that these were platforms 12 and 13. The main up platform was platform 8 (N & S) and the main down platform was 9. The next through platform was 14 (currently 9) while the two on the outside were 15 and 16 (now 10 & 11). As I recall, the platform you are referring to was used for the DMU stopping service to Darlington and Newcastle which used to run in those days but also, occasionally, for Harrogate trains.
Pretty much spot on. I'm a York man myself and up until the remodelling in about 1987(?), the layout was:
Platforms 1-3. South facing bays on up side of main trainshed. The current platform 1 is all that remains here (was previously 3), although the
original platform 1 had been lifted many years before I became interested in the railway.
Platforms 4-7. Bays facing the Scarborough line. So many platforms because Hull services used to terminate in them as well in steam days. By the 1980s, only 6 and 7 were in any regular use, with 4 and 5 used to stable stock. Platform 7 survives as the current platform 2, the rest now a car park.
Platform 8. Very long platform encompassing what is now 3 and 4. Roughly speaking the current 3 was 8A and 4 was 8B (northbound facing the Scarborough line only). Because of the centre roads, a southbound train could depart from 8B while another train was sitting in 8A.
Platform 9 was the current platform 5. Was originally longer and, like platform 8 was subdivided into 9A and 9B, which could also be separately accessed from the centre roads. When the station was remodelled, it was truncated at the north end to reduce the severity of the curve on the ECML.
Platforms 10 and 11 were south facing bays on the down side of the main trainshed. Now platforms 6 and 7.
Platforms 12 and 13 were north facing bays on the down side. Platform 13 survives as platform 8, still performing its main function as the Harrogate bay. The now trackless and truncated (other face of the former platform 9B) platform 12 was occassionally used by Harrogate trains, and by the handful of local York-Darlington DMUs that ran then.
The remainder is simple: the current platforms 9-11 were 14-16, although there was a centre road between 14 and 15 then.