A UK registered Aircraft is operated in accordance with the UK ANO wherever it may be in the World. The licensing requirements for that aircraft are contained in the UK ANO. Art 62(1) validates any valid ICAO licence to allow you to operate that aircraft on a private flight under conditions specified in the Article. There is no territorial limit imposed in Article 62, so you can do it anywhere in the World. Nothing to do with anyone else!
Deeming a non-United Kingdom flight crew licence valid
62.—(1) Subject to paragraphs (3) and (4), paragraph (2) applies to any licence which authorises the holder to act as a member of the flight crew of an aircraft and is granted—
(a) under the law of a Contracting State other than the United Kingdom but which is not a JAA licence; or
(b) under the law of a relevant overseas territory.
(2) Subject to paragraph (4), for the purposes of this Part, such a licence is, unless the CAA gives a direction to the contrary, deemed to be a licence rendered valid under this Order.
(3) Paragraph (2) does not apply to such a licence if it authorises the holder to act as a student pilot only.
(4) A licence deemed valid under paragraph (2) does not entitle the holder—
(a) to act as a member of the flight crew of any aircraft flying for the purpose of commercial air transport, public transport or aerial work or on any flight for which the holder receives remuneration for services as a member of the flight crew; or
(b) in the case of a pilot’s licence, to act as pilot of any aircraft flying in controlled airspace in circumstances requiring compliance with the Instrument Flight Rules or to give any instruction in flying.
(5) A JAA licence is, unless the CAA gives a direction to the contrary, a licence rendered valid under this Order.
You have no problem whatsoever operating that aircraft. One thought however, as you have a FAA Pilot Certificate which of course has no RT privileges outside the USA I presume you have a FCC Radiotelephone Certificate Form No FCC 605-FRC