Thanks for the pointer. It's an interesting read.
I think the answer is "It depends" and "Are you being a d*ck or obviously p*ssed".
Clearly not illegal by UK law at time of press.
Being allowed to consume alcohol but not being allowed to be drunk is a bit like being allowed to eat food but not be overweight. If you want a definition of drunk see above.
The intention here is that we don't have a safety problem with intoxicated passengers. This happens frequently and an airline that ignores it is not meeting their duty of care. Setting down a standard for this is going to be difficult. A complete moron who downs 2L of duty free vodka in 30 mins and causes a diversion due to their behaviour is clearly committing a criminal offensive. On the other side of the scale a frequent traveller who has 50 or 100mL of their favourite beverage that isn't available for BoB so should not be dissuaded. A set of three people who crack open a bottle of rum and go through it with free cokes and ice I can see as being either side of the line. I have certainly drunk more than that in CC monitored beverage distribution and only once in 30 travelling years on BA been told 'last one' but never actually denied.

"Should not" rather than "Must not" because its not illegal so they can't stop you (provided you're not drunk). "Should not" so they deter weak willed rule followers, thereby increasing the market for their BOB offering...

Call me a cynic...