What an interesting mystery!
The tiara worn by the Duchess of Northumberland certainly looks identical to the one worn by Queen Dina.
In June 1955 Queen Dina and King Hussein visited the UK for an official visit for which a dinner was held at Downing Street. I couldn't find a photo showing the Queen from the front, but it seems to my eye that she was wearing a different tiara for that event.
Any suggestions as to which one it might be?