It really depends what is considered streetwear.
I consider some Gucci, Prada, Paul Smith Jeans, PS by PS, John Varvatos USA, Marc by MJ, Rag & Bone, Raf by RS, Vince, Steven Alan, BoO and YSL high-end streetwear.
Most of those are known for suits, pea coats and other high end items but they do make sneakers and clothes that can qualify as streetwear to me.
Some people classify streetwear as just tee and jeans with sneakers though while I classify streetwear to include along with tees, sneakers and jeans, sport shirts, chinos, the occassional leather shoes such as bucks/oxfords or boots and coats like pea coats and sport coats.
I wouldn't really classify BBC or Ice Cream high-end though, just expensive. That might just be me though.