FAR 61.51 says: A private or commercial pilot may log PIC time if that person is "the sole manipulator of the controls of an aircraft for which the pilot is rated".
I am the sole manipulator. I am rated for the aircraft on my ICAO (UK PPL).
What gives?
Adam, I don't know what "standalone" means, but insofar as the regulation goes, ratings you may hold on another ICAO certificate are irrelevant.
The regulation refers to the holder of an FAA private or commercial pilot certificate. If you're rated on a given aircraft under another nation's regulation, then your logging of that time will be done in accordance with the regulations governing the nation (or conglomerate of nations) that issued your pilot certification.
When considering what the FAA allows you to log, understanding that the FAA regulation regarding logging applies only to the holders of FAA-issued pilot certification, you can see that the regulation is talking about FAA Private Pilots and FAA Commercial pilots.
As a student pilot, however, you may log PIC when solo. If you're a private pilot who is rated in the airplane (meaning you hold category and class ratings on your FAA certificate), you may log the time spent as sole manipulator, as PIC. Category and class for a Cessna 172, for example, would be Airplane (category), Single-Engine Land (Class).
You can log all the time you wish on another nationalities pilot certificate or license, but you'll need to do so according to the regulations of the nation that granted your pilot certification. When logging time on your FAA certificate, you'll need to log the time according to the regulations (and ratings) applicable to your FAA certificate.