From another thread I learned that a ticket is regulated (roughly: restrictions cannot be increased, and price rises are controlled) if an equivalent ticket existed in 2003.
So did the unavailable short-distance tickets, mentioned above, not exist in 2003? Or is there a another clause which says that tickets below a certain distance are not regulated?
It's a bit more complex than that. To form a Regulated Fare, a relevant fare in the eligible category for the specific train company must ordinarily have existed at the September 1995 fares setting round. The only absolute check that a fare is regulated is to find out if it is included in a particular TOC's fares basket. These have been supplied in the past in connection with FOI requests but trust me, unless you have lots of free time you don't want to trawl through one!
Going back to BR days, in general there did not use to be off peak singles as the accepted wisdom in the travel trade was that a single journey was almost always by definition less 'elastic' (i.e. optional) than a return one. As market based pricing took over from the old strict mileage based charts, the problems arose when an off-peak return fare was set below a peak single fare, meaning that some customers asking for a single were actually sold a return. Trust me, as a booking clerk at the time, this did not generally enhance BR's reputation amongst it's customers. ('What' I hear younger forum members cry 'We are always told that all the problems of today are caused by nasty privatised TOCs and that BR was a benevolent institution loved by all!').
Anyway, as a result, a 1993 enhancement to the BR fares system allowed an algorithm to be set up that created 'off-peak' single fares where the off-peak return was cheaper than the full fare single. For Savers, this was £1 less than the Saver return, and for Cheap Days, it was 10p less, so the 'off-peak' title was a bit of misnomer, but it did stop returns being sold when the passenger just wanted to go one way (and apparently curbed the trade in Glasgow pubs for the sale of unused return portions).
The prevailing philosophy has been turned on its head in the last 15 years by the rise firstly of the low-cost airlines, and then by Advance fares on TOCs. Both of these make use of real time demand management and compulsory reservations to work out yields and demands and (hopefully) set appropriate fares.
DfT fares regulation is still stuck in 1995 so hasn't really got to grips with any of this. There is currently a fares and retailing review being conducted by the DfT to examine, amongst other things, whether and how the regulatory mechanism could be updated.