I've been to several coffee shops which have power sockets around the walls (probably been there decades) and power sockets set into some of the tables. None of the sockets are labelled as being for public use or not, but everyone uses them without complaint.
Same with one of the restaurants at Heathrow Terminal 3 - they have a row of seats facing a counter along the wall. Each of those has a power socket, obviously for customer use, but none are labelled as such.
If anything, given that some sockets on trains are specifically labelled as not for public use, it's fair to assume that those with no label are available for all to use. Especially if there's a single socket next to every seat...
Same with one of the restaurants at Heathrow Terminal 3 - they have a row of seats facing a counter along the wall. Each of those has a power socket, obviously for customer use, but none are labelled as such.
If anything, given that some sockets on trains are specifically labelled as not for public use, it's fair to assume that those with no label are available for all to use. Especially if there's a single socket next to every seat...