By chance, I discovered the photo below showing Princess Marina, Duchess of Kent wearing 2 of the smaller floral elements (now in Princess Alexandra's tiara) as hat brooches.
The occasion was the arrival of the Shah of Iran on a State visit in May 1959. I believe that these elements are the two small floral elements seen below the larger central element.
The million dollar questions are --
Do the elements come from Queen Mary? Princess Victoria? Louise, Duchess of Argyll? Or some one else?
1959 Arrival of the Shah, London, May 1959
Detail from the image above
Still from a Pathe video of the arrival
The tiara showing the smaller floral elements near the Princess' hair.