I'd first heard the Duke of Edinburgh, was one of the early adopters of mobile phones in a book by Jon Agar called constant touch .http://www.ucl.ac.uk/sts/staff/agar/documents/agar_constanttouch ........on amazon
the book says he had one in his lagonda coupe sports car that could communicate using admiralty frequencies via a pye relay station on the hamstead hills direct to buckingham palace.
A search of the http://www.london-gazette.co.uk/issues/41273/supplements/67 revealed that PYE got a royal warrant to the HRH for the first time in Jan 1958.
One gets a warrant after 5 years, so it was approx 1953, when he got his.
The royal website confirms this .. http://www.royal.gov.uk/ThecurrentRoyalFamily/TheDukeofEdinburgh/90facts.aspx
83. The Duke had an early version of a mobile telephone, made by Pye Telecommunications of Cambridge, fitted to his car in 1953. He installed an improved version provided by the AA (of which he was President at the time).
And the PYE museum website give us model details here http://www.pyetelecomhistory.org/photos/warrant/warrant.html
In the Early 1950s, Pye Telecommunications installed the PTC112 remote mount mobile into the car belonging to HRH Prince Philip, The Duke of Edinburgh. Later this was replaced with the higher power PTC114 and subsequently with other radiotelephone products.
There is a nice technical tour video of the PTC112 here http://www.youtube.com/watch?v=UC-9KGmIiy4
And some technical descriptions here ... http://www.pyetelecomhistory.org/prodhist/mobiles/mobiles.html#PTC112-113_1950