The Royal collection site lists Vandyk as the photographer of the 1927 picture.
I assume this is Carl Vandyk: https://en.wikipedia.org/wiki/Carl_Vandyk
He was a London photographer, who according to the national Portrait Gallery had his studio on the Buckingham Palace road and had several Royal Warrants. After his death the business was continued by his son.
Thus I think we can conclude the pictures were taken in London, and as you suggest it might have been a formal portrait commissioned before the Australia trip. The Royal Collection lists the picture as acquired by QEII. Perhaps she acquired the signed version from someone who received it as a gift during the trip?
Edit: I did not see your follow-up post about the November 1926-dating before I posted this. It confirms the date and photographer.
--Previous Message-- : Thank you Nellie and Torkel : : Nellie, I think that perhaps in the photo : showing a single pendant that QEQM may be : wearing her turquoise earring used as a : pendant, but I am not 100% sure - mainly : because the brooch or brooches are : definitely not turquoises as the stones are : too dark, and HM did not usually mix jewel : colours, except when she wore her 4 Cartier : bracelets. If you look at the media reports : I posted you will see that one talks of a : diamond pendant, but whether HM had such a : large diamond then is something I have no : knowledge of. : : Date of photo. : : Thank you Torkel. Your reasoning is a joy. I : have just found another version of the photo : in the Royal Collection site. It is dated : 1927; that is certain as it is signed by : QEQM and dated in her own hand. Of course : the photo may have been taken somewhat : earlier, after June 1926 or December 1926, : as you argued. : : : http://www.royalcollection.org.uk/collection/search#/414/collection/2508458/the-duke-and-duchess-of-york : : I have a slight suspicion that the photo may : be from the Australian trip, so tomorrow I : will try to see if I can match a description : of HM's evening dresses to the one shown in : the photo. One thing which makes me wonder : about when this photo was taken is that the : Royal Collection site says it was acquired : by QEII. If a set of photos had been : commissioned in London before the 1927 : Australian trip, I would expect that the : royal collection would have copies so I am : considering if the photo was taken overseas : during the 1927 trip. It may not necessarily : have been taken in Australia as the royal : couple went to New Zealand and Fiji and : perhaps other places. : : Edit: I think that the emerald drops have : different shapes and are slightly different : sizes. : : : :