If you live in the West Midlands

[cocksstrideintheevening]

Is it West Midlands or west midlands? I'm proofing something and our 'house style' has changed it to lower case. I disagree!

Apparently north east, south east, north west etc are lower case because they're not named counties. It's annoying me.

I’ve always used capitals

Surely it should have capitals because it's a name of something

West Midlands if referring to the county. west midlands if referring to the area in general