I know that the Oasis indoor market in Birmingham has a rockabilly stall on one of the upstairs levels I think... it's pretty well advertised in the window as you go buy, can't remember what it's called though.
There are a few vintage stores:
There's Yoyo which is off New Street
Yo Yo, Birmingham - Birmingham venue review - Itchy Birmingham Guide
and the Yellow vintage shop in Digbeth which I'd say mostly sold 70s/80s clothes but there are some gems occasionally. They have some amazing vintage furs if that's your sort of thing.
Vintage superstore Fashion Dummy
The only other thing I can think of is the Saturday (and now Sunday) Flea at the Custard Factory (also in Digbeth, a little further down the road from Yellow Vintage) which has some vintage sellers.
www.custardfactory.com
xx