A nice bit of LH-relevant dialogue from Alan Hollinghurst’s The Line of Beauty, which is every bit as good as jamessal said:
“So where’s your father’s shop, Nick?” said Pete.
“Oh, it’s in Barwick—in Northamptonshire?”
“Don’t they pronounce that Barrick?”
“Only frightfully grand people.”
Pete lit a cigarette, drew on it deeply, and then coughed and looked almost sick. “Ah, that’s better,” he said. “Yes, Bar-wick. I know Barwick. It’s what you’d call a funny old place, isn’t it.”
The class and regional/local implications of the pronunciation of place names is one of the things I find most bewildering about UK language and culture. For what it’s worth, my Daniel Jones Pronouncing Dictionary (13th ed., 1967) gives only the “Barrick” pronunciation. Of course, that presumably refers to one or more of the other Barwicks; Wikipedia recognizes places of that name in Devon, Hertfordshire, Norfolk, Somerset, West Yorkshire, and North Yorkshire, but none in Northamptonshire.