I do not think Queen (Mother) Elizabeth wore the Hanover pearl necklace at her husband's Coronation in 1937. If we compare these two pictures (on the second one, we know that Queen Elizabeth II is wearing the Hanover pearls), we can count, from the bottom of the longer row to the shoulder's curve where the necklace is not visible anymore, approximately 28 pearls on QEQM, and 18 pearls on QEII. And I have the impression that the Hanover pearl necklace is slightly shorter than the one worn by QEQM in 1937, and also made of slightly larger pearls.
This relies only on my visual impression, though...