I would also add Joseph to the list. It's not fashion-led, but does do well-cut wide trousers, good knitwear etc.
One thing I would very definitely do if I were to set up a capsule wardrobe from scratch is to consider what colours you like wearing best, & also what shapes & fabrics, types of patterns etc that you're keen/not keen on. If you're not sure what colours suit you best, you could consider a colour analyst?
I know that for some people colour isn't that important - but for me I get great pleasure from wearing, say, a jumper that's in the absolutely perfect shade of pea-green, or dark red, or inky blue for me. It really lifts my mood & makes me happy! It also preferably has to be a lovely wool/alpaca/cashmere/mohair knit, & of course in a fit & style that I love - one that goes with many things I already own.
If you are cutting the contents of your wardrobe right back, & considering spending not inconsequential sums of money on new pieces, then I would want each one of those items to be utterly perfect ...!!!
It's not dissimilar to what I tell clients with small gardens. If they love, say, ornamental crab apples & only have room for one - then it has to be the perfect one. The variety that flowers longest/is the exact shade of pink to tone with the nearby tulips/has the most dramatic & long-lasting fruits. And I will always hand-select the specimen with the best form for them.
I think you should apply similar principles to your new capsule wardrobe!!