If by AP you mean advance purchase tickets then the picture is far more complex than you suggest. The recent Passenger Focus report is well worth reading on this matter and highlights some interesting facts.
For example, just what pax really pay to travel compared to the highlighted 'full open' fares:
London - Cardiff:
Full fare £79. 75% pay £40 or less. 50% pay £30 or less. 25% pay £20 or less
London - Manchester:
Full fare £115. 75% pay £45 or less. 50% pay £35 or less. 25% pay £25 or less
London - Edinburgh:
Full fare £126. 75% pay £55 or less. 50% pay £40 or less. 25% pay £30 or less.
This fact is very good but please take off your rose tinted specs, you can't dispute that only the minority of passengers can buy and use AP tickets! I will need to look up the report but if I recall it is less than 2% of journeys made have access to advance purchase fares! I am sure that for example not a single journey made with Northern (to name one TOC) offers an advance purchase fare. 50% of people are season ticket holders, yes they get discounts from the full fare but they have also had massive increases of their tickets! Season tickets discounts over full fare haven't altered since BR days.
We have people that use CDR tickets, again they have had massive increases as the ticket is unregulated. They also have had restrictions put on in the evening peak by FCC and XC to name 2. You can't get an AP ticket from Potters Bar to London, a journey more people do than London - Edinburgh!
I guess the full fares quoted above are singles as I know the open return is in the region of £250 for London - Manchester. If you look at the £67 saver return however, it has also had the restrictions when it can be used altered making it less useful. Small comfort to that some people pay £25 (single) or less when you are now forced into paying £250 or picking a less suitable time! Who would pay the full open fare to Edinburgh, the only train you can't use the saver on is the 0550!
From my local station previously if I needed to be in Birmingham by 0930 I could use a saver and travel on a direct train. Now it is an open return and I need to change twice! More money for a service which is a lot worse! Infact I can't even get to Birmingham by 0930 anymore now the direct trains have gone. Can I get an AP for this journey no chance?
Most people are paying more; BR also did AP's I used to use the Super Advance a lot. If they didn't have them on London - Scotland routes then everyone would fly. As stated more people use CDR / SDR than AP's, so the cheap fares the minority get are frequently quoted by ATOC and passenger focus but at least passengers focus does admit the majority have no access to AP's!
Someone also mentioned increases to frequency, again this are limited to IC to routes some routes have had cutbacks since privatisation. I know I live on one! I am sure to a lot of passengers the single direct train per day from Berwick - Oxford was preferred compared to the situation now with lots of trains and 1 connection. People prefer direct train, not only because they know they will get to their destination without been stuck somewhere due to a missed connection, but they also prefer not having to haul baggage between trains, over footbridges etc!
Snapper - to some of the other points since.
BR did cut back many IC routes in preperation for privatistation - I admit this freely, I am not going to hunt every IC cutback, I have already proved my point.
Satisfaction on the ECML route has been higher than the WCML ever since the Pendo's came on on-line. source passenger focus. Maybe I do have a point, try asking some passengers which they prefer!
Finally BR increased services during boom years, look at the past and you will see this. We have just been through a boom period. No we are hitting bad times we cutbacks are also happening. But look at the number of line reopening 10 years either side of privatisation, BR did much better on that front! Did GNER talk about Leeds every 30 minutes in 1996 no, it wasn't until they knew demand had grown, so how would BR be able to predict that far in the future?