In fact, all of these replies are correct in some ways.
The following is copied from the US Embassy website :-
Passport Validity: If traveling under the Visa Waiver Program, the passport must be valid for at least 90 days from the date on which the holder enters the United States. If not, the holder will be admitted until the expiration date on the passport. Note: Passport holders from Andorra, Brunei, and San Marino must be in possession of a passport valid for at least six months from the date of departure from the United States, even if traveling visa free under the Visa Waiver Program.
If you have a UK passport, you can travel under the Visa Waiver Programme (subject to other restrictions, for example if you have criminal convictions). When you go through immigration in the US, your passport will be stamped with a date that you are permitted to stay until ie 90 days after tha date of admission. The problem obviously arises when your passport is not valid for another 90 days - but the advice seems to be the date will be adjusted to reflect this. I just don't think I would ever want to take that chance!
In short, if you travel in May and your passports expire in September, you should be fine anyway, but FYI I'm pretty sure that the UK Passport Service will add on up to 9 months unexpired from an old passport to a new passport - I think they set this up a while back to deal with people applying at the last minute and causing backlogs etc.
Enjoy your trip!