Are you specifically looking for more affordable clothing chains? Like their "versions" of Forever 21, Express, Abercrombie & Fitch, etc.?
From what I have read, I would say the UK equivalent to Forever 21 is Primark, while their H&M/Zara is Topshop/Topman...
Having said that, I've only personally shopped Topman at Nordstrom. Its initial ticket is high compared to H&M, and NOTHING is tumble dry, but they do take massive markdowns on it.
I am also personally dissapointed with the (mens) merchandise selection at Cotton On, who claim to be "the H&M of Australia".
Thanks for the info! More like Zara.