It seems to me a lot of people haven't bothered to check up what the law actually says, and have assumed it goes further than it actually does.

But I'm still puzzled why there should be any requirement to have no smoking notices in any enclosed premises open to the public now that there is a national ban on smoking in such places.

I imagine it's based on some idea that, in the absence of such notices, it might be possible for someone to argue that they didn't know smoking was banned - but that just seems ridiculous. I can't imagine how any court could accept such a defence.

It'd be rather as if someone being done for driving at 80 mph, on a road where the National Speed Limit was in force, were to try to claim that they thought the National Speed Limit was 80 mph. "Well, there weren't any notices indicating the maximum speed allowed". Fat chance!