A slice of ham cut extremely thin, to increase yield to the seller. The name was given because of the association of very thin slices with the catering at the Vauxhall gardens in London. It seems that in the Gardens there was a restaurant which acquired a reputation for its “plate of ham”. The ham had to cover the plate, and was, of course, extremely thin.
There was a tale told of a chef who applied for an advertised situation with one of the Vauxhall caterers, and gave as one of this qualifications that he could carve a ham so that the slices would cover an acre. He was rejected. The requirements were that the slices from a ham must be thin enough to cover two acres, The term Vauxhall slice came to be used for any thin piece of meat.
From The Baker’s ABC by John Kirkland, formerly Head Teacher of National School of Baking, published 1927 by Gresham