Under the plans, which are said to have the support of the Government, all minor members of the Royal Family will also lose the right to use royal cars, aircraft and trains at taxpayers' expense and there will be more contact with the public, especially through visits to hospitals.
Only the Sovereign's closest relatives will retain the HRH titles, and among the nine members of the family set to lose are the Duchess of York's two daughters Princess Beatrice and Princess Eugenie.
The proposals, put forward in memo form by a senior Palace official, reccomends that in future those stripped of their HRH titles may be known simply as "Prince X" or "the Lord or Lady Y". The memo adds that in due course the HRH titles should eventually be restricted to the children of the Sovereign and the children of the heir to the throne.
The Queen has been discussing plans to modernise the monarchy with the Way Ahead group of senior advisers. And Tony Blair's goverment is said to be encouraging the Royals in this process.
Older member of the Royal Family, including the Queen Mother, however, are said to be worried by the pace of change.
The Queen has already decided to start paying tax, and recently agreed to break a centuries-old tradition by saying that first-born daughters should have the right to succeed to the throne, taking precedence over their younger brothers.