It is the pilots responsibility to be aware of what route he has filed and the service he is likely to receive as a result.
I think you would find that if you lined up 100 really experienced international IFR pilots, including any number of airline pilots, all flying GA planes, (but not residents of Goodwood, Shoreham, Lydd, etc) and got them all to develop (let's skip for now how exactly they are going to do the "development") a route which does not get chucked out by CFMU, from say middle of France to the middle of the UK, and then got them to fly it on a clear day, you will find that most of the unpressurised ones will settle nicely at say FL100, and about 99% of them will fall for this trick of being transferred to London Information
I have had this a number of times (before I sussed the simple work-around which is to force a handover from Paris Control to London Control, by leaving France not below FL120; this requires oxygen but I always have that anyway) and not once was I told anything about leaving controlled airspace. The system assumes that everybody is a local hack.
The word "information" is not really a sufficient clue that your IFR clearance has been terminated, because in France you can be flying on a Eurocontrol flight plan, at say FL080, Class E, and get a seamless radar service. Then if you want, due weather, a climb to FL150, you get a transfer to Paris Control, and the seamless service continues.
If you have a pragmatic ATC system, where everybody has radar, there is no operational need to drop traffic the moment it leaves CAS.
The UK could do the same if it wanted to, but what's happened is that the "professional pilot controllers" have nailed their flag to Class A airspace, which works OK in the UK but this system is not used anywhere else. Only Italy has so much Class A but Italy is a mess anyway.
Also, for all the rules which CFMU runs, most of which bear little relation to what ATC operates on the day, if Country X was dumping an IFR clearance on traffic leaving CAS, then CFMU should reject such routings - but it doesn't
