From Clubs and Club Life in London, published 1899:

This noted house, which faced the north gate of the old Royal Exchange, was long celebrated for the excellence of its soups, which were served at an economical price, in silver. One of its proprietors was, it is believed, John Ellis, an eccentric character, and a writer of some reputation, who died in 1791.

This 18th century map positions the northern entrance of the Royal Exchange as being opposite Bartholomew Lane, so I’ve assumed this tavern was close to that.