Upvote:3
I believe you are referring to an article similar to this one from The Guardian which the British media have been reporting since 5th May 2016.
You are right in thinking that the US 'may' turn away British passport holders if they do not have a biometric passport. However it sounds like you do have a biometric passport which were first issued in the UK in Spring 2006 so you should be fine. If you have this symbol on the front of your passport then it is biometric.
If in doubt I would contact your local passport office to clarify. There are several around the UK. If there is an issue then the passport office can create a new passport the same day (at a cost) in time for your pending flight to the US. It sounds like there is some confusion with dates being reported by the British media.