As a Tory sympathiser, she is seen as a good candidate for the position following the appointment of Gavyn Davies as chairman.
Davies, the millionaire Goldman Sachs economist, was made chairman in September and is close to key members of the Labour government. It has been reported that the government is seeking a Conservative as deputy in order to counter Tory claims that BBC management is being filled with the Prime Minister's supporters.
The director general of the BBC is Labour supporter Greg Dyke.
Neville-Jones, 62, has been a BBC governor since 1998. Supported by the Conservative lobby, she became the first woman to chair the joint intelligence committee, which oversees MI5, MI6 and GCHQ. She was a Foreign Office diplomat for more than 30 years, reaching the position of deputy under-secretary. She left to join NatWest bank as managing director following her work as a senior negotiator during the Bosnian War peace talks.
Following NatWest, she took the position of vice-chairman at Hawkpoint partners, a division of NatWest.
The vice-chairman of the BBC usually has different political views to the chairman. Other suggested candidates for the job have included Michael Portillo, following his failed bid for the Tory leadership, and Virginia Bottomley, the former Tory health secretary.
Following the appointment of Davies, shadow media spokesman Tim Yeo said, "The BBC belongs to the public who, through the licence fee, support it with very large sums of money. In return, they expect the highest standards and independence from government. Because of this, and the authority attached to the BBC output, it should at all times be, and be seen to be, politically objective. There should always be distance between it and the government of the day."
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