The London Hospital was, and is, on the Whitechapel Rd, so it was convenient and nearby for Lusk to take it there.
Mrs Marsh's description was of a 6 foot man with dark hair and beard and an Irish accent. He refused to go to the Crown Hotel to leave a message, the Crown being the HQ of the Whitechapel Vigilance Committee. Perhaps he was a Temperance advocate!
Strangely enough, Lusk complained to the police in October that his house was being watched by a 'sinister' bearded man. He requested police protection.