According to Roberts Queen Alexandra left her Dagmar necklace to the Crown and QEII has been photographed wearing it so I assume the cross is with QEII.
Another image showing Queen Alexandra wearing it
QA may also be wearing it in this image.
The Duchess of Gloucester wears a diamond cross which resembles Queen Alexandra's but I do not know if it is the same. Princess Margaret also wore a diamond cross but I do not have a photo.