The picture was taken on 28 May, during one of the garden parties hosted by the Queen at Buckingham Palace.
Princess Michael recently underwent an eye operation (cataract?), hence the black patch covering her eye, and giving her quite the "pirate look"...
Regarding the brooches, I can not clearly identify them. There seem to be yellow stones, but I do not remember having seen this pair of brooches earlier.
Unfortunately, on this large pic, we can not see the brooches. But we can get a good look onto the Princess' earrings and pearl necklace - quite whoppers too!
During this same garden party, the Queen wore on her pink coat one of her diamond floral sprays - the one with pink diamonds, that she wore for the first time in July 2012 for a reception at Buckingham Palace marking the opening of the London Olympic Games. Princess Anne wore a two-row pearl necklace, and a large modern gold and diamond brooch (I think I have already seen this brooch, but I can't find pictures in my files).