The Royal Navy and Royal Air Force were created directly by the monarch through a Royal Charter as a single entity.
Does the RN have a Royal Charter? I am not sure it does. The RN is quite different to the RAF in its formation and terms of service. In the RN no contract is signed by new officers (not sure about the ratings) nor an oath of allegiance given. Acceptance of the "Queen's Shilling" i.e. pay, is deemed sufficient enough "contract". Whereas in the RAF I think both a contract is signed and an oath given.
I think this is also why an RN officer never formally "retires" as such, he or she is placed on the retired list of officers but retain the entitlement to placing "Royal Navy" as a post nom, whereas the RAF have to put RAF(Retd).