It just needs to be valid for the period you plan to be there, assuming you are a UK passport holder applying for a visa waiver on arrival.
The actual rule says 90 days (which is the standard admission period for a visa waiver) but there is a concession for UK (and some other) passport holders that if the passport is not valid for 90 days, they will only be admitted for as long as it is valid.
Ignore anyone who spouts out 6 months - that is rubbish.