For the 1st picture (November 1938): I am not sure, but I would guess Queen Victoria's Fringe Brooch (aka the Waterfall Brooch), but the fringes are hardly visible:
Off topic: the Teck Loop Necklace, here worn as a tiara, is absolutely splendid! I hope it will find its way back to the main branch of the Royal family...
On the second picture: I would guess Queen Victoria's Fringe Brooch again. The large central diamond seems visible, as the twelve diamond surrounding it.