The recipient of a doctorate conferred by a university or other body, such as the Council for National Academic Awards, is entitled to be addressed as 'Doctor'. The exception to this is a surgeon, who is known as Mr/Mrs/Miss, etc.
In practice, when a well-known figure outside the academic world receives an honorary doctorate, the recipient does not generally adopt the title of 'Doctor', especially when he or she already has other styles or titles, for example a peer, an officer in the Armed Forces, a judge, etc. This, however, is a matter of the recipient's choice.
It is also a matter of choice whether the appropriate degree(s) should be placed after the name on an envelope, or whether to address the recipient as 'Dr John Smith' or 'Dr Mary Smith'.
By custom, however, a Doctor of Divinity always has the letters DD appended after the name, because many recipients - such as an archbishop or bishop - are not normally addressed as 'Dear Doctor Johnston'.
In the University of Oxford the appropriate letters are usually omitted, and the envelope is addressed 'Dr James Johnston', irrespective of the particular doctorate.
In the University of Cambridge both forms are used, and in the University of London the letters to signify the particular doctorate are usually given. It is, however, recommended that the letters, where known, are used in order to distinguish him or her from a medical practitioner.
The Very Rev James Johnston, DD
The Lord Blank, DLit
Sir Henry Robinson, MusD
John Smith, Esq, LLD
Mrs Joan Smith, PhD