The morning one that missed York but stopped at Darlington was a Newcastle starter, either the 0630 or 0700 ex Newcastle if my memory is correct, with a York starter catering for the York passengers. Similarly the 1700 down was followed by a 1703 Newcastle which called at York and elsewhere.
The timetable I was thinking of:
Northbound:
0800 The Scottish Pullman (York & Newcastle) 3h59 - to Glasgow, 5h10
1000 Flying Scotsman (Peterborough, York & Newcastle) 4h08 - to Glasgow 5h05
1400 The Scottish Pullman (York & Newcastle) 3h59 - to Glasgow, 4h57
1700 The Scottish Pullman (Darlington & Newcastle) 4h08
Southbound:
0630 The Scottish Pullman (Newcastle & York) 3h59
1500 The Scottish Pullman (Newcastle & York) 3h59 - from Glasgow, 4h59