This is from Hansards, the official source for Parliament (and, as usual, the Daily Mail gets it wrong)
Oral Answers to Questions
Deputy Prime Minister
The Deputy Prime Minister was asked—
2. Mrs Helen Grant (Maidstone and The Weald) (Con): What plans he has to bring forward legislative proposals on the rules governing succession to the Crown. 
5. Mark Lancaster (Milton Keynes North) (Con): What plans he has to bring forward legislative proposals on the rules governing succession to the Crown. 
The Deputy Prime Minister (Mr Nick Clegg): We are working closely with the New Zealand Government to secure the agreement of all the Commonwealth realms to the introduction of UK primary legislation on royal succession. Legislation will be introduced once we have secured this agreement and when parliamentary time allows.
Mrs Grant: If the birds and the bees of the romantic Isle of Anglesey were to conspire and bless our future King of England and his wife with the patter of tiny feet before this law was enacted, and if that royal baby turned out to be a little girl, would she succeed to the throne?
The Deputy Prime Minister: If the birds and the bees were to deliver that blessing to the Duke and Duchess of Cambridge—and, indeed, the nation as a whole—that little girl would be covered by these provisions and changes to the rules of succession, because they operate as from the time of the declaration at the Commonwealth summit last October. It is important to remember that the rules are de facto in place, even though de jure they still need to be implemented through legislation in the way I have described.
Mark Lancaster: Will the Deputy Prime Minister confirm that there are no plans to change the requirement for the monarch to be a communicant of the Church of England?
The Deputy Prime Minister: There are no plans whatsoever.
Paul Flynn (Newport West) (Lab): In the interests of democracy and dragging the monarchy and the office of Head of State into the 21st century, can it be arranged for the new Bill to permit alternative candidates to stand as Head of State, given the misgivings about King Charles III?
The Deputy Prime Minister: The hon. Gentleman mentions what sounds like another attempt to resurrect the alternative vote system, which I do not think was greeted with universal acclaim last year and would not apply in this area either. More seriously, I do not think he should belittle the enormity of this change. We are getting rid of some very long-standing, discriminatory anomalies on male primogeniture and the rule preventing heirs to the throne from marrying—uniquely among all religions—Roman Catholics. That is real progress that has not been achieved in a long time.
Most people do not realize that the 1917 Letters Patent does not include the HRH and the title Prince or Princess for the younger children of the eldest son of the Prince of Wales. This means only the eldest son of of the eldest son of the Prince of Wales will be entitled to the HRH and the title Prince.
But in view of the forthcoming changes to the succession, it seems probable that this Letters Patent will also be superseded in order a distaff heiress to have royal style and titles during the lifetime of her great-grandmother.