Actually, Princess Anne - as the Sovereign's daughter - does have precedence over the wife of the Sovereign's grandson.
I believe it is by generation, blood first. When Princess Anne became Princess Royal she became the senior Princess in the country. Previous regents also moved up the daughter of the Princess royal. ex: Edward VII
The Official Order of Precedence
- Queen Elizabeth (The Queen)
- The Princess Royal (the Sovereign's daughter)
- The Duchess of Cornwall (the wife of the Sovereign's eldest son)
- The Countess of Wessex (the wife of the Sovereign's younger son)
- The Duchess of Cambridge (the wife of the Sovereign's grandson)
- Zara Phillips (the Sovereign's granddaughter)*
she might place after Eugenie but definitely before Autumn
- Princess Beatrice (the Sovereign's granddaughter)
- Princess Eugenie (the Sovereign's granddaughter)
- Autumn Phillips (the wife of the Sovereign's grandson)
- Lady Serena Stanhope (Wife of the Sovereign's nephew)
- Lady Sarah Chatto (Sovereign's niece)
- Princess Alexandra, The Honourable Lady Ogilvy (Sovereign's cousin)
- Birgitte, Duchess of Gloucester (Wife of the Sovereign's cousin)
- Katharine, Duchess of Kent (Wife of the Sovereign's cousin) Didn't she also convert to Catholicism
- Princess Michael of Kent (Wife of the Sovereign's cousin) *Catholic so is excluded
- Lady Louise (the Sovereign's granddaughter)* minor & is not included
The Private Order of Precedence (which is entirely at the Sovereign's will):
- Queen Elizabeth (the Sovereign)
-
Princess Anne (British Princess by birth)
- Princess Alexandra (British Princess by birth)
- Camilla, The Duchess of Cornwall (British Princess by marriage)
- Sophie, The Countess of Wessex (British Princess by marriage)
- Zara Phillips
- Princess Beatrice (British Princess by birth)
- Princess Eugenie (British Princess by birth)
- Catherine, Duchess of Cambridge (British Princess by marriage)
- Autumn Phillips
- Lady Louise (British Princess by birth) *Minor is not included in precedence.