Well, you've got the ANO article itself, which states that any ICAO license is valid on a G-reg, within the limitations stated. What art. 62 means by "Contracting State" is any state contracting to ICAO, which is essentially all of the civilized world.
The only other bit of text you need is the ICAO article/annex/whatever, that states that ICAO states will accept any aircraft for overflight/landing/whatever where the flight crew has a legal, valid and current license under the laws of the state of registry of the aircraft. Or wording to that effect.
In other words, if the UK deems your combo G-reg/FAA license to be legal, then other states are supposed to accept it as such.