Pre-privatisation (and pre-lead up to privatisation, as I remember fares increasing during that time as privatisation approached) walk up fares were generally quite reasonable. If there were advance fares, I never used them. Back in the day, it was pretty normal to decide on the spur of the moment you'd go and visit somewhere and the trains were a great facilitator of that at that time.
I doubt the internet would have been a factor as to the introduction, as if cheap fares were available people would use the telephone to book (or phone to check availability and go to the station booking office, that's how we rolled back then).
I also don't think the focus was on the tickets being "competitive" but more trying to find ways of moving the majority of passengers to pre-booking. If you imagine a predominantly pre-booked railway you have a railway in which you can deploy the minimal rolling stock possible to convey those passengers, while also being able to vary prices according to different times of day and push people for the very most they are able to pay.
Edit:
If memory serves, BR essentially had three tiers of Advance Purchase tickets:
- SuperApex - Book up to 14 days in advance
- Apex - Book up to 7 days in advance
- SuperAdvance - Book by 6pm (2pm for some early morning trains) the day before travel
Ah yes those ring a bell and in fact I think I did get a SuperAdvance once or twice. As I recall there was no limit on availability like with today's tickets, nor variable prices, simply that if you booked in advance the price advertised was the price you got. In fact, I think the SuperAdvance didn't even restrict the train to use (might be wrong, but pretty sure it was just like a super off-peak).