The second picture raises more questions. Like the above this comes from the collection of the Imperial War Museum but in this case it is actually identified as W.S.Morton's Fish Shop. However, you might note that the slab from which the fish are being served is supported by what looks like a solid front while in the former picture the slabs are on legs. Also the same wall of the shop is shown in both pictures but appear to be very different - note the absence of the decorative tiles in the second picture (there is evidence for decorative tiles in one of the pictures of Arthur in my post.)
Also in the first picture the slabs seem to be further back. My person feeling is that the first picture depicts the shop but it is the second picture that is actually captioned as Morton's by the Imperial War Museum so I remain confused.