Article 26 4(a) is one part of the jigsaw, but don't you also need to heed para 11 as well ??
(11) Notwithstanding anything in this article:
(a) the holder of a licence granted or rendered valid under this Order, being a licence endorsed to the effect that the holder does not satisfy in full the relevant minimum standards established under the Chicago Convention, shall not act as a member of the flight crew of an aircraft registered in the United Kingdom in or over the territory of a Contracting State other than the United Kingdom except in accordance with permission granted by the competent authorities of that State;
(b) the holder of a licence granted or rendered valid under the law of a Contracting State other than the United Kingdom, being a licence endorsed as aforesaid, shall not act as a member of the flight crew of any aircraft in or over the United Kingdom except in accordance with permission granted by the CAA, whether or not the licence is or is deemed to be rendered valid under this Order.
Does a FAA PPL have an endorsement placed on it under the Chicago Convention ? [para (a) would then apply]
I am thinking specifically about the fact that the FAA Class 3 Medical does not meet the standards.
Paragraph 2.3.1.6 of Annex 1 to the Chicago Convention requires that private pilots should hold a Class 2 medical certificate. The US has filed a difference to this standard which states that "Private pilots shall meet the requirements of an FAA Third Class Medical Certificate, which does not fully comply with the ICAO Class 2 Medical Certificate." This can be found in the Supplement to Annex 1.
If that is still the case then para 11 (a) only allows you to fly a G reg in the UK. You'd need the ruling of the contracting State if you wished to fly a G reg elsewhere on a FAA PPL.
My interpretation anyway
PS
Englishal got this response from France
I also wrote to the French authorities and asked if I could fly a G reg aeroplane on my FAA ticket into French airspace. They said that as long as the CAA allowed me to fly the G reg, then they would as well.