An NHS number was a personal identification number, related to the public health service in the United Kingdom, the National Health Service.
In 2008, when the Tenth Doctor was a patient at Royal Hope Hospital under the alias "John Smith", his name was linked to an invalid NHS number. (PROSE: The Secret Lives of Monsters)
In 2010, the Eleventh Doctor showed Craig Owens his "NHS number" along with his "National Insurance number" and a reference from the Archbishop of Canterbury, when introducing himself to move in as Craig's flatmate. Each piece of identification was, in fact, merely the Doctor's psychic paper at work. (TV: The Lodger)