I got my Uzbek visa in Almaty , back in november 2006. No problems at all, apart from the week spent waiting for it (they didn't keep my passport during this time) no LOI required, I just copied the names of some hotels from someone's guidebook into the form.
That was with my Italian passport;for Brits it might be different, I'm quite sure that they ask for a LOI from americans.
Hope this helps.
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