Things can get quite confusing about these "diadems".
I do agree that the second pic in aigrette's link http://members2.boardhost.com/royal-jewels/msg/1423933826.html does show Queen Adelaide wearing the Diamond Diadem 1820 made for George IV, and which Queen Elizabeth II wears to and from parliament in our own time. What a history for a piece of jewellery!
In my post above, "her new circlet, the Grand or Regal Diadem" refers to the regal circlet made for Queen Adelaide and remodelled, twice, for Queen Victoria. It was worn by Queen Alexandra and Queen Mary before being stripped of all diamonds to make the crown for Queen Elizabeth (who became the Queen Mother). The empty frame of that regal circlet seems to now be with the Royal Collection, after a period in the Musem of London. What another history for a piece of jewellery.