Ofcom, the official body of the UK governing spectrum usage, says itself that as a CEPT member itself it applies the CEPT recommendation T/R 61-01, which recommends:
that CEPT member administrations recognise the principle of the CEPT radio amateur licence issued under the conditions specified in Annex 1 and Annex 2, on which the administrations of the countries visited will not levy administrative charges or spectrum fees
So, your license is accepted as long as you visit. Your nationality should make no difference.
That is very much the spirit of the cept recommendations - make it easier for people traveling, regardless of what their passport says, to do radio.
Note that you would have to check with ofcom's actual norms how that would look in detail, but come on: for this to become a problem, someone at ofcom would have to
- Find detailed regulations surprisingly making an exception that puts visiting UK citizens at a disadvantage,
- Look up your US call sign
- Correlate the name they get with a UK citizenship catalog, something that they probably don't even have access to for this purpose
- Have reasonable cause to assume that there's only one Natalie Downe between the US and UK, and that it's you
- Cause minor problems for you
(Southern states accent) Ain't nobody got time for that, (posh English accent) to be quite honest, dear.