You could try online, but if you're as fussy as me then you'll want to try stuff on before you buy it.
The menswear in new look is good quality, fairly priced. Though most of the time republic is expensive, they often have sales on and they're generally cheap.
Personally, I'd suggest getting all your basics from primark. Then getting the not-so-basic things from places like new look and republic, like jackets and stuff.