Charles Tyrwhitt is a long way down the list, quality-wise, but when they are almost always offering 4 shirts for 100 quid (if I have that British Pound symbol, I can't find it) you can get some decent shirting on the cheap. The 'sea island quality' shirts are much nicer fabric, and priced accordingly. Stay away from Thomas Pink shirts, though. They are at the bottom, quality-wise for English shirts, but a slick website and marketing means they charge much more than they ought to.
I've never been a big fan of non-iron ... it's a chemical that's applied to the material, basically, and it wears off with repeated cleanings, so you end up eventually with a non-non-iron shirt.
I would disagree with your statement about CT shirts, the one's that I have are very well made but they are not the bottom line CT shirts. I do agree about Thomas Pink shirts, terrible quality, especially for what you pay!
Yes, the wrinkle-free chemical does wear off in time but I've had several shirts for several years and they still look great. I prefer to buy wrinkle-free because I prefer to do shirts myself and spend a couple of minutes doing a little touch-up.