Originally Posted by
Whopity
... without a licence [the student] cannot legally fly the aeroplane [solo] in the UK.
It could surely be done with CAA permission (article 151(3) of ANO 2016) subject to a favourable interpretation from the Office of Chief Counsel for FAA on the meaning of 14 CFR 61.89(a)(5). The relevant clause in the US regulation states that a "student pilot [certificate holder] may not act as pilot-in-command of an aircraft [o]n an international flight."
I would contend that an international flight requires flight in the airspace of more than one state consistent with the definition established in article 96 of the Chicago Convention for an international air service. The US has used a similar definition, again for the unrelated purpose of an international air service, in 14 CFR 61.3(j) among others. The same definition was adopted in the Tokyo Convention in 1963 at the insistence of the US representative (Shubber, Sami. 1973. Jurisdiction Over Crimes on Board Aircraft. Pp 256–258.)
If FAA is of the opinion that 14 CFR 61.89(a)(5) disallows a solo training flight wholly within the airspace of a single foreign country then there is still a relevant ICAO Annex 1 standard, supported by 49 USC 40105(b), which states that a "student pilot shall not fly solo in an aircraft on an international flight unless by special or general arrangement between the Contracting States concerned."
Would UK CAA really turn down an opportunity to sell such a permission?