Half past a quarter to, just struck a bobby.

[sigma]

When I was little I remember my grandmother giving this response when asked the time.
Where did it originate from.

[inksplotter]

"Just struck a Bobby" is called a Wellerism. Named after Sam Weller in Pickwick Papers, it means an irrelevant phrase at the end of sentences. The most famous is "As the actress said to the bishop." Half past a quarter to is interesting, it basically means "shut up, I've no idea."