Conventions certainly do vary, geting. The Times may have relaxed its approach now, but it was always the rule before. Here's part of an article from 2010.
"No living persons except the Queen (or King!)" is an ancient tradition of The Times UK Crossword. No crossword clue, either in its solution or wordplay, makes reference to a person alive.
The Times may have good reasons for this restriction: to keep the crossword away from expressing political leanings (as many clues about politicians do), or to avoid giving celebrities free advertisement. The rule also wards off potential embarrassment that can ensue if a clue making flattering reference to a famous person is closely followed by the some appalling discovery about that person, or a clue poking fun at a celebrity is published on a day that person meets with some misfortune.
Other British crosswords like the Guardian, Independent and Financial Times are relaxed about this rule. An old Guardian clue by Araucaria, which made a topical reference to Jeffrey Archer, is perhaps the best known of its kind:
Poetic scene has surprisingly chaste Lord Archer vegetating (3, 3, 8, 12)
This clue was published in the Guardian at the time Jeffrey Archer was lying low at his property, The Old Vicarage Grantchester, after the notorious scandal. The answer, THE OLD VICARAGE GRANTCHESTER, is an anagram of (chaste Lord Archer vegetating)*. The word "surprisingly" not just functions as anagrind but also makes a tongue-in-cheek statement about Archer's character.
The clue also finds mention on the Wikipedia page of The Old Vicarage, Grantchester."