A very carefully worded advertisement indeed.
The only advice is to ask exactly what the final piece of paper will be.
My money is on an FAA licence which is indeed OK for flying G reg aircraft in the UK and is indeed accepted in every ICAO country but provided that you are flying an N reg aircraft
"A British School" - Hello, hasn't the USA been independent for a few hundred years? This is a US school targeting British students!
Regards,
DFC