It has to be somebody like Exeter; you cannot just call up London Control directly unless you have just filed a Eurocontrol IFR flight plan (
AFAIK).
However, this ought to be done in plenty of time. It can take 5-15 mins IME to get an IFR clearance into Class A, on a Eurocontrol flight.
I never never succeeded in getting a "popup" clearance into Class A in the UK, but crossing a small piece of it is a different thing.
you can only transit the base at right angles to it
Don't you think that is a stupid rule?
Apart from anything else, ICAO says that the boundary between two airspace classes taken on the classification of the
less restrictive of the two, so the base of a typical UK piece of Class A is Class
G.