I have in front of me the WI cook book, 1984 edition.
Their recipe for Yorkshire parkin contains:
6oz plain flour
1 1/2 tsp sod bicarb
1 tsp ground ginger
2oz medium oatmeal
3oz brown sugar
3oz maragarine
4oz golden syrup
1 egg
milk
Lancashire parkin, on the other hand, contains:
8oz oatmeal
3oz plain flour
1tsp ground ginger
2oz brown sugar
pinch salt
1/2 tsp (scant) sod bicarb
4oz marg or lard
8oz golden syrup / treacle
2 1/2 fl oz milk.
On that basis I wouldn't bother with the Yorkshire version.