If you don't want to mess with the UKBA, I think the easiest thing is to keep your FLR, ILR and US passport in your maiden name and just apply for citizenship in your married name.
As ksand said, as long as your US passport and BRP match, you can apply for citizenship in whatever name you want. Take a look at the citizenship application and it says you just need to show support for applying in a name different from your passport (like a marriage cert).
After I asked the same question last year, that's what I've decided to do. :-) Of course, if you want kids before you apply for citizenship and you want everything in your married name by then, it's different. :-)
