If you are concerned that there is not much time left on your passport, then I would guess that it is not machine-readable. Starting from 26th October 2004, if it is not machine-readable, you will need a visa.
I would suggest that you get it renewed (you will be issued with a new one which will be machine-readable) and you will be able to take advantage of the Visa Waiver scheme (and just fill in those forms they will give you on the plane).
I thought you need as much time on your passport to cover your visit to the US. In other words, your passport has to be valid when you return to the UK. As said, the UK has a visa waiver scheme with the US so we don't have to get a visa (unless you have a criminal record, or something).