@Eenuh unfortunately my sister buys the majority of her clothes through high street stores. I just assumed she was an online shopper as I haven't accompanied her in a long time.
She did give me some names though. Wallis (also has a sale ending in 40 minutes time), New Look, Monsoon, Peacock, Dorothy Perkins, forever 21 and like you alread mentioned above, Asos.
Could you perhaps elaborate "easily order clothes from"? Do you mean easy as in registration? the actual process of purchasing products?
Sorry I couldn't be of more help.