I am an Indian national and was refused a UK visa in 2009 in NYC and given a 10 year ban, but now I'm a US citizen.
Would the ban still apply if I wanted to visit the UK?
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The ban is not against your passport, it is against you the human being bearing the passport and hence regardless of whichever different nationalities you assume or acquire (barring somehow acquiring British or EU citizenship), the ban remains in effect.
If you decide you still want to visit the UK after your ban is over, make sure you get entry clearance to ensure a smoother (your landing is virtually guaranteed to be a bit rocky regardless of whether you get entry clearance or not because of the ban which is a serious black mark) landing process when you arrive in the UK although you are allowed visa free entry as a US citizen. Attempting to enter visa free can lead to much grief as happened to another recently naturalized American UK visitor in a somewhat similar situation to yours.