I've been following Make It British, and found two interesting brands, Eyato and Isabella Queens. Prices aren't cheap (~£600 to £1500) but they aren't as high as mainstream brands can be. Both bag brands are made in London, and Isabella Queens has UK leathers. Eyato also offers bespoke services (as well as bespoke shoes and outerwear). Eyato has unique design style, and Isabella Queen more classic.
http://www.eyato.com/bags/4593957926
https://www.isabellaqueen.co.uk/shop/
(A non-bag recommend from Make It British: Elizabeth Martin Tweed has some pretty clothes at great prices!)
Gosh they're different, I must take a closer look, TY