BR was losing shedloads of money, and that was a comparatively new experience for both it and the Government - it had been losing money for 10 years, since 1952 to be exact. Until then the railways had been profitable, some more, some less, for some 130 years so this was seen as the natural order of things. However the loss was getting bigger from year to year and passenger numbers were sliding. It was essential to cut costs as the Government was also limited in the amount it could spend on the railways in view of all its other commitments. (Some things never change!)
You suggest that cost control measures should have been tried. There is no denying that BR was sometimes slow in introducing these but one has to consider what was possible in days of jointed bullhead track and manual signalling without spending large sums on continuous welded rail and centralised signalling, and that on a loss-making railway.
Using the figures quoted the route had earnings of £90,400 with movement expenses (direct costs of running the trains) of £84,400. That is, there was a margin of £6,000 per year. (These sums seem small, but £6,000 in 1961 is worth the same as £100,000 now).
The terminal expenses, that is the cost of running the stations including a proportion of the costs of the shared stations, York, Beverley, Cottingham and Hull, amounted to £23,100 and the track and signalling for the 42 miles came to £43,000. Together these two items come to £66,100.
So, in order that people would still be able to travel from York to Hull via Beverley (and vice versa) without sending them via Selby and without them becoming a burden to the taxpayer it would be necessary to make the operation of the route cost neutral, i.e., that BR would not make a loss, but would not make a profit either. If this were to be the case with the revenues and movement costs remaining the same (the trains were mostly newish dmus so the costs of operation had already been reduced), the costs of stations, track and signalling would have to be reduced from £66,100 to £6,000 per year. This is a factor of ten.
I leave it to the reader to work out how this could be done.