Posted by one Dave Richards on Grammar Girl
It is a fallacy to claim that standard British English uses single quotation marks first and doubles only for quotes embedded in quotes. This is indeed the case with novels, but all other publications use double quotation marks first and singles for nested quotations.
As a Brit, I agree. I don't see a lot of single quote marks in print. But I don't read many novels.
The British preference for single quote marks in novels is simply because novels often have a lot of reported speech. Why clutter the page up with twice as many of the ubiquitous little ticks?
We use single quotes just the same as Americans when it means 'so-called', for example. We just listened to Henry Fowler's sensible suggestion (in 1908) that we should reverse the then-dominant "single quotes within double quotes" convention for nested contexts. But only for things that are likely to need it (basically, novels).
EDIT: Comparing British and American instances of what they call a in Google Books (where it's often followed by a "quotated" term), I don't see any clear-cut tendency for either corpus to favour single or double quotes, so I'm not particularly defending that point. It seems to be a 'personal' rather than 'national' stylistic choice (but I admit mixing the two as here doesn't look good! :)