You must not have been to the UK for a long time then.
Simply enter the passport you are showing to the airline in the API (or the airline will do it for you if you don't). In any case, if you are entering the UK with a UK passport, nobody is going to care that a US passport was provided in the API.
Five years-ish. e-Borders (or whatever it's called) was about to come in, I think.
So, basically, keep doing what I've been doing?