When the National Speed Limit was invented I think there were three major differences to today - firstly, drivers were generally expected to have some kind of common sense, I know plenty of NSL roads where it isn't safe to do 60mph, though you could also argue that the NSL was brought in precisely due to a lack of common sense.
Secondly, most cars were significantly underpowered compared with today's models and had (in comparison) poor handling and brakes. A bottom-of-the-range Corsa or Fiesta bought today will significantly outperform mark One versions of the same, and they were only launched in the 1970s - cars from the 1950s were even worse. It would have taken a lot longer to reach those high speeds, and if you regularly drive a car where you have to stand on the pedal to get it to slow down, you naturally become more cautious.
Aside - there was an interesting related comment on last week's Top Gear where some actor was driving fast around the track and nearly lost it on a bend. Video showed the car "squirming", brake lights coming on briefly and a slight growling noise, before it settled down. Chris Harris said "ooh, saved by the computer there", to which said actor was aghast, thinking that it was their own driving skill that had saved the day. I'm not a professional driver, but to me it looked like a classic example of an Electronic Stability Programme deciding to brake selectively in order to stop the rear end of the car swinging around. People rely on these aids, so much that they don't notice when they apply.
Aside to the aside - my eldest is learning to drive, as is a nephew. Both have been told (by different instructors) that it is not necessary to apply the handbrake at traffic lights or a "stop" line. This is exactly opposite to what I was taught in the 1980s and (trivially, perhaps) does make hill starts somewhat awkward... except that many, many cars have "hill start assist" these days.
Thirdly, there was just generally less traffic about. You probably had more pedestrians (and animals) to worry about, but tooling across the moors at 60mph, slightly mis-judging a bend and ending up on the wrong side of the road is less likely to have ended up with you heading straight for oncoming traffic than it is today.
Just my 2p. I could rant all day, and I say that as someone who recognises that their own driving leaves quite a lot to be desired.