The Swan is not strictly in All Hallows. There is an entry in the 1901 census, which is then crossed out, and in fact is listed under St Margaret Pattens & St Dunstan in the East! It can be listed here for brevity. The pub was rebuilt in its present form in 1898. ***
A listing of historical London public houses, Taverns, Inns, Beer Houses and Hotels in All Hallows Lombard Street parish, City of London. The All Hallows Lombard Street, City of London Public House Trade Directory uses information from census, Trade Directories and History to add licensees, bar staff, Lodgers and Visitors.

Swan Tavern, Ship Tavern Passage, EC3 - in August 2007
Kindly provided by Stephen Harris
The following entries are in this format:
Year/Publican or other Resident/Relationship to Head and or Occupation/Age/Where Born/Source.
1869/Henry George Bacon/../../../Post Office Directory ****
1870/H Bain/../../../Guildhall Library ***
1884/Peter B Harris/../../../Post Office Directory ****
1891/Hy Page/../../../Post Office Directory ****
1894/Robert Murrell/../../../Post Office Directory ***
1895/George Clark/../../../Post Office Directory ***
1899/George Summer Shaw/../../../Post Office Directory ***
The 1901 census lists the address as the Swan. 47 Eastcheap, but I believe
this is correct.
1901/George S Shaw/Boot Maker & Licensed Victualler/37/Bristol/Census ****
1901/Alice Shaw/Wife/31/London/Census
1901/Florence Shaw/Daughter/14/Shoreditch, London/Census
1901/Archibald G Shaw/Son/12/Shoreditch, London/Census
1901/Victoria A Shaw/Daughter/3/Shoreditch, London/Census
1901/Ernest H Shaw/Son/1/City of London/Census
1921/Levy & Franks/../../../Post Office Directory ****
*** Provided By Stephen Harris
**** Provided By Kevan