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"Cheapest" depends on what you hold and how often you move it. A platform with no fees at all can still be the expensive option if it charges a percentage every time you convert currency to buy an American share.
The ordering below is by total cost for a typical portfolio, not by headline rate — the modelled figures further down show why those two answers differ. Each platform's cheapness also comes with a constraint, and those are named.
No platform fee and no dealing commission, with currency conversion low enough not to matter for most people.
Platform fee Free · UK dealing Free · FX 0.15%
No platform fee and no conversion charge — the cheapest here on paper, provided ETFs are all you want.
Platform fee — · UK dealing Free · FX 0%
Very low currency conversion, plus interest paid on cash sitting uninvested.
Platform fee Free · UK dealing Free · FX 0.1%
No platform fee and commission-free dealing, with conversion costs between the others here.
Platform fee Free · UK dealing Free · FX 0.5%