Places cheaper than primarkWatch
Asda/Tesco basics and clothing sales
Also Forever 21 is amazing value - really nice stuff for great prices, and they have great sales too. Just after Christmas they were doing a 3 for 2 thing on all their sale stuff, which was already up to 50% off, so I got tons of stuff for hardly anything. They do "flash deals" every day as well, and have sale items most of the time. I got some amazing skinny jeans for £8 the other day (Primark's are £9) - gotta be my favourite shop ever
You can also get lucky in TKmaxx - the have a section called modbox or something which sells their nicest (ie most fashionable ) clothes so its worth a look if there's one nearby.
I find that supermarket clothes really aren't that cheap, and are really bad quality. Same for Peacocks - most of their stuff is horrible.
Internacionale sells some really nice stuff, and their sales are so good, but they don't do online and their non-sale stuff can be really expensive.
But yeah, I'd recommend just checking sale items of well-known shops (even Topshop and River Island can have some great deals), especially online as it's easier to find what you want, and they're more likely to have your size.