The Duke of Cambridge is the eldest son of the Prince of Wales. According to the 1917 Letters Patent, only his eldest son would have the style and title of HRH Prince. (All children would move to royal status once Charles succeeded to the throne.)
A new law regarding the succession to the throne is about to be promulgated. This law will allow for the first born to succeed regardless of sex.
Earlier today, Queen Elizabeth II issued a new Letters Patent where 'all the children of the eldest son of the POW should have and enjoy the style, title
and attribute of Royal Highness with the titular dignity of Prince and Princess prefixed to their Christian names.'
House of Lords, London SW1A 0PW
31 December 2012
The QUEEN has been pleased by Letters Patent under the Great Seal
of the Realm dated 31 December 2012 to declare that all the children
of the eldest son of The Prince of Wales should have and enjoy the
style, title and attribute of Royal Highness with the titular dignity of
Prince or Princess prefixed to their Christian names or with such other
titles of honour.
C I P Denyer