I was flying a Cirrus last week which has a built in telephone. It uses the Iridium network of low orbit satellites rather than a ground based system common to other mobiles.
I was going to suggest that too; I have used the Thuraya system myself for getting airborne weather data (tafs, metars, radar images) but not myself used it for voice (it needs a connection into the intercom to work properly).
I did once get an incoming call (I was on the ground) from a friend at FL300 over Greenland, using his Iridium phone, and while it was legible the quality was extremely poor, which I think is fairly typical of satellite phone systems. I wonder if this is normal...
installed in an aircraft
registered in the United Kingdom or carried on such an aircraft for use in connection
with the aircraft
Didn't look up the context (in the ANO context is everything) but "installed" means installed in the aircraft, and "in connection with the aircraft" means exactly what??
This is why you cannot permanently install e.g. a satellite phone in an aircraft, without a load of paperwork.
You can install the satphone rooftop antenna (e.g.
page 7 here) easily because one can get them with Approved Data e.g. TSO. However, the phone and its "car holder" don't normally come with Approved Data so that part is normally mounted in a "temporary" manner. I am sure there are fully approvable systems and maybe the Cirrus is one such - presumably this was an N-reg Cirrus? I'd imagine getting this through EASA would be a nice gravy train for somebody.
This looks interesting...