OS
You have what is known as 'Indefinite Leave to Remain' - you probably knew that. It means that you are regarded as settled in the UK though you do not (probably because you had no reason to apply for it) have British Citizenship. The visa that is stamped in your old US passport continues to be valid and is the critical thing that UK Border Agency staff want to see at immigration control each and every time you return to the UK. Unless the US authorities return you to old passport at any time, you can continue to use it, and the stamp contained in it, as the required evidence of your right to be in the UK indefinitely.
If you require to transfer the visa stamp into your current US passport for any reason then there is a fee - £169 currently for a postal application.
Most of what I know about this can be found at this webpage.
http://www.ukba.homeo...fer-visa-to-passport/
BM