Advance single for 5th November
£2 on Northern, £7.10 on LNER.
Would such a variation have applied in British Rail days?
Apex tickets were not available for such relatively short journeys in BR days, and neither were they this cheap. Ordinary walk-up tickets would have been a more reasonable price, such that there would be no reason to want Apex tickets for this kind of journey.
But pricing differentials very much did exist between routes seen as better served and worse served - with those which saw new stock and an increase in service frequency (e.g. Great Western main line) seeing an increase in fares (which is why even the regulated Reading-London SVR is an absurd £28.30, for a return journey taking from just 26 minutes!). Equally, fares along routes that were poorly served, e.g. the Heart of Wales line, were set at a much lower level.
In many ways this differential pricing still exists today, e.g. with 'via Llandovery', 'via Hereford' etc. fares undercutting the Any Permitted substantially for some journeys, as well as having more lenient peak restrictions, if any.
But in terms of differential for an Advance ticket I don't think there is anything you can compare this to. I don't think that it's particularly unfair to charge a significantly higher fare for the LNER service, as the stock is likely to be significantly more comfortable, you are guaranteed a seat (which you are not on Northern, as the Advances use 'counted place' quotas), and you are taking what could be the seat of someone who might be travelling a much longer journey, e.g. Leeds to London. LNER have fewer seats left over for higher revenue passengers such as these so I think it makes sense that they make you pay proportionally more if you really want to travel on their train.