Depends....
You would ask your current service provider to gig it up for you and they should transfer you to the approprate agency that could sort it out for you.
It might well be that Exeter "has" that bit of airspace so can give you the transit or will be able to get you a clearance depending on thier workload. If you were not talking to anyone a request to london info would get you transfered to the approprate agency.
And if you can't get through to anyone due to RT saturation london Mil is always a good joker to have in your back pocket down that way and can usually clear you across without transferring you.
Now please bare in mind my experence is doing this sort of thing in a Multicrew CAT Turboprop I presume you would get the same responce as GA.