I've just called the Ministry of Justice with a nagging thought.
Royal Mail was created by Royal Charter, I believe by Henry VIII. Presumably, selling off a segment to private ownership would require that the Royal Charter be amended. I looked for previous examples of private sector organisations with Royal Charters, and the only ones I could come up with were incorporated as private organisations with a Royal Charter. Now they tend to be used only for public sector organisations, professional bodies, universities and charities.
Royal Charter is dealt with by the Privy Council.
However, the Royal Charter is not the reason that Royal Mail is called Royal. The RSPCA used to be the SPCA, until it was 'made Royal'. The use of the descriptor 'Royal' in an organisation or company's name is determined by the Department of Constitutional Affairs-as-was, which is now the Royal and Hereditary Branch at the DCA (now subsumed within the Ministry of Justice).
I just called them directly, and they didn't seem to appreciate my call, and told me that I had to speak to the MoJ Press Office. Central Government Departments have very nice people answering the phones in their Press Offices, so they have said they will get back to me.
My questions were:
Should Royal Mail be partially or wholly privatised, will it still be permitted to use the term 'Royal' in its name?
What activities need to be undertaken for this to remain permissable?
What actions have been taken by Government Departments, in particular the Department for Business, Enterprise and Regulatory Reform, to address this issue?
The Press Office at the MoJ say they will get back to me.
UPDATE: I've just spoken to a lovely lady at the Privy Council Office, and they assure me that the Royal Mail doesn't have a Royal Charter. Either it never did (though I thought it was established with one), or it was revoked, perhaps when it became a publicly-limited company, limited by guarentee of the Government.
Curiouser and curiouser.
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