Okay, upon re-reading I think I need to modify a bit what I wrote earlier. Here’s what the CMS (section 7.15) actually says:
Civil, military, religious, and professional titles and titles of nobility are capitalized when they immediately precede a personal name, as part of the name:
President Buchanan
<snip>
Note that when such titles are used in apposition to a name they are not part of the name and so are lowercased:
the emperor Maximilian (i.e., the emperor who was Maximilian)better: President François Mitterand of France
So it would seem that in CMS style, one would refer correctly to “Prime Minister Blair,” but you would still say “British prime minister Tony Blair.” In the first case, “prime minister” is a title and capitalized as such.
It goes on to add:
[Sections 7.17-7.18]In text matter, titles following a personal name or used alone in place of a name are, with few exceptions, lowercased.
<snip>[e.g.] Frederick Lord North, prime minister of England; Lord North; the prime minister of England; the North ministry
<snip>
[Section 7.23] For sake of clarity, or perhaps unbreakable tradition, some British titles are capitalized when used without a personal name:
Prince of Wales
but: prince consort
British usage favors a more liberal use of capitals for titles than that recommended above.
And I guess in at least one case, a more liberal use of no capitals.
Having a quick look around, it appears that both India and Australia use PM as a title.
The only other British style guide I can find is that of the Times (far more conservative than the Guardian):
President (of any country, also President of the European Commission), cap at first and all subsequent mentions when used as a variation for a specific person, eg, "George W. Bush said that … the President said that … "; “Richard Nixon was the President until 1974”. Lower case when using president more generally, eg, “Richard Nixon was the 37th president of the United States”…
Prime Minister cap for every country, but only in reference to a specific person, eg, "Tony Blair said that … the Prime Minister said that … "; “Margaret Thatcher was the Prime Minister from 1979 to 1990”. Thus lower case when using prime minister more generally, eg, “Being prime minister has affected many men’s health”; “This is a prime minister with much still to prove”. …
…which, as far as I can see, is actually more caps-happy than the CMS, giving us “British Prime Minister Tony Blair”.
