I don't have Pigot's 1823 London Directory, but from the 1825 edition:-
Custom House, Thames Street
Foreign Business Department, Officers Inwards: Clerk of the Warrants, E. H. Clark
Waterside Department, Officers Inwards, Searchers: John Clarke, ...
Excise Office, Broad Street
Inspector General of Permit Printing Paper, F. Clark
From the general pages of occupations
Agents-Navy: Goode and Clarke, 15 Surrey St, Str[and?]