tinanam0102“Could I ask if "a quarter to eleven" a British usage?”
In speech (especially), I tend not to use "a"; I'd just say, for example, "it's quarter to eleven". In speech (though not so much in writing), the use of "a" feels slightly fussy or old-fashioned to me (though it doesn't leap out as a glaringly odd thing to say). I'm not sure if this is typical of British English speakers or if it's just me, but from memory I think many people in my part of the world omit "a".
Apart from the caveat about "a", this is very common usage in Britain.