One of the previous owners of Mulligan’s, James Mulligan, was known to have a very strong connection with the Theatre Royal, which stood opposite the premises. He ran the family business from 1875 until this death in 1931.
Among papers found in Mulligan’s, one is a playbill announcing the appearance of a world-famous magician, Louis (Ludwig) Döbler. The notice dates from August 1842 when Döbler performed at the Theatre Royal.

This suggests, but does not prove, that there may have been a connection between the premises and the Theatre Royal going back to the mid-nineteenth century.
Döbler was an Austrian engraver-turned-magician. He first applied electricity to magic, opening his act in spectacular fashion by using concealed wires to ignite simultaneously the turpentine-soaked wicks of the 100 candles that lit the stage.