As already said, Kings go to their Coronations wearing their Caps of Estate. In the photograph from 1911, one can see the Bishop of Baths and Wells holding George V's.
Queens Regnant also go 'covered', and Victoria and the present Queen both wore the Diamond Diadem.
George IV was the exception. His Coronation in 1821 was so flamboyant (he wanted to eclipse Bonaparte) that he had the Diamond Diadem made and proceeded to ruin the effect by wearing it over a hat with so many feathers that it was practically obscured.
Queens Consort go bear-headed. The very odd thing that Queen Alexandra did was wear a pair of gloves but that is another thread!
Sovereigns and Queens Consort do not wear crowns before the Coronation. Thus, Edward VIII never wore one and certainly not to open Parliament in 1936. The situation did not arise in 1937, as the State Opening took place some months after George VI and Queen Elizabeth were crowned. At the 1952 State Opening, the present Queen wore the Diamond Diadem throughout (along with Queen Victoria's Parliament robe, as her own was under construction and first worn to the Coronation).
Queens Dowager have attended only in 1937 (when Queen Mary set the precedent) and 1953. On both occasions, they wore their own crowns (minus the arches) throughout. This is logic, as they were both already-crowned Queens.
There is no question of Sovereigns and Queens Consort donning robes or changing head-dress in the Annexe: how they left the Palace is how they went up the aisle. A small point in 1953 is that the Duke of Edinburgh didn't wear his Coronation robe to/from the Abbey but he wasn't, of course, being crowned. And the Queen didn't carry her nice boquet that accompanied her in the coach up to the Theatre, where it would only have got in the way!
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