It is a daguerrotype really but they are early photographs so that counts. This came my way from Iconic Photos, a site I had not been aware of. It has now been bookmarked. The picture dates back to 1844 and was made by Antoine Claudet, one of the pioneers in the field and a student of Louis Daguerre.
Having acquired a share in L. J. M. Daguerre’s invention, he was one of the first to practice daguerreotype portraiture in England, and he improved the sensitizing process by using chlorine (instead of bromine) in addition to iodine, thus gaining greater rapidity of action. He also invented the red (safe) dark-room light, and it was he who suggested the idea of using a series of photographs to create the illusion of movement. The idea of using painted backdrops is also attributed to him.
From 1841 to 1851 he operated a studio on the roof of the Adelaide Gallery (now the Nuffield Centre), behind St. Martin’s in the Fields church, London. He opened subsequent studios at the Colosseum in Regent’s Park (1847–1851) and at 107 Regent Street (1851–1867).
It looks like the photograph of the Duke of Wellington was taken at the studio behind St Martin’s in the Fields. There were several subsequent paintings and etchings of the Duke made from Claudet’s photograph but none of them are quite as good as the original. As it says on Iconic Photos:
The photo itself taken in 1844 was a remarkable bridge across centuries. Memories of Elizabeth the First or the English Civil War were as fresh and recent to Wellington (born 1769) as Wellington or Lincoln is to us. The photo was different from latter paintings and engravings based upon it — unlike the kindly old man which smiled down from the paintings, the photo showed a crankier, more determined Wellington — a face you truly expect from the Victor of Waterloo.
I think it might be this portrait by Abraham Solomon, listed as being by an unknown artist here, that is meant here. It is not nearly as good as earlier portraits or the photograph, which is well worth looking at carefully. The only problem is that while it is easily available on the internet, I have not been able to find out where the original is.