This is the earliest street directory I have found so far which also includes publican detail.
London Street Listings in 1832.
Abbey street, Bermondsey
Abchurch lane, Lombard street
Abchurch yard, Cannon street, City
Abdy street, Horselydown
Aberdeen place, Edgware road
Abingdon row, see Goswell street
Abingdon street, Westminster
Acorn street, Bishopsgate
Acton street, Grays Inn road
Adam & Eve court, Oxford street
Adams court, Old Broad street
Adams mews, Charles street, Grosvenor square
Adams place, see Kings road, Chelsea
Adams place, High street, Borough
Adams row, see Hampstead road
Adam street, Adelphi
Adam street East, Portman square
Adam street, W, Bryanston square
Addington place, see Camberwell road
Addington square, Camberwell
Addington square wharf, Camberwell
Addle Hill, Doctors commons
Addle street, Wood street
Adelphi terrace, Strand
Agar street, Strand
Air street, Piccadilly
Albany Court yard, Piccadilly
Albany road, Old Kent road
Albany street, Regents park
Albany terrace, see New road, Marylebone
Albemarle street, Clerkenwell
Albemarle street, Piccadilly
Albion buildings, Bartholomew close
Albion place, London wall
Albion place, see Battle Bridge
Albion place, see Blackfriars road
Albion place, Walworth road
Albion street, Rotherhithe
Albion terrace, New North road
Aldenham terrace, Pancras road
Aldermanbury, London wall
Aldersgate street, St Martins le Grand
Aldermary Churchyard, Watling street
Aldgate High street, Whitechapel
Aldgate within, Leadenhall street
Alfred mews, Tottenham court road
Alfred place, Bedford square
Alfred place, Newington causeway
Alfred row, see Spa road, Bermondsey
Alfred street, Bedford square
Alie place, Great Alie street, Goodmans fields
Great Alie street, Goodmans fields
Little Alie street, Goodmans fields
Allen street, Goswell street
Allerton street, Hoxton New town
Allhallows Churchyard, London wall
Allhallows lane, Upper Thames street
Allington street, Pimlico
Allsops buildings, see New Road, Marylebone
Allsops buildings, see Great Dover street
Amelia place, see Walworth road
Amelia street, Walworth road
Amen corner, St Pauls
America mews, Minories
America square, Minories
America terrace, see Kings road, Chelsea
Amwell street, Pentonville
Anchor street, Spitalfields
Anchor & Hope alley, Wapping
Andersons buildings, see City road
Angel court, Friday street
Angel court, Skinner street
Angel court, Throgmorton street
Angel court, Great Windmill street
Alex place, see New road, Pentonville
Angel street, St Martins le Grand
Angel terrace, see New road, Pentonville
Anns place, see East street, Walworth
Anns place, Hoxton Old town
Ann street, Pentonville
Apollo buildings, see East street, Walworth
Arabella row, Pimlico
Arbour terrace, see Commercial road
Archer street, Great Windmill street, Haymarket
Argyle place, Regent street
Argyle street, New road
Argyll street, Regent street
Little Argyle street, Regent street
Arlington street, Piccadilly
Arlington street, Sadlers wells
Artichoke row, see Mile End road
Artillery court, Chiswell street
Artillery lane, Bishopsgate street
Artillery passage, Bishopsgate
Artillery place, Finsbury
Artillery place, Westminster
Artillery street, Bishopsgate
Artillery street, Bermondsey
Artillery terrace, Westminster
Arundel street, Panton square
Arundel street, Strand
Ashby place, see Commercial road
Ashby street, Northampton square
Upper Ashby street, Northampton square
Aske street, Hoxton
Assembly row, see Mile End road
Asylum buildings, see Westminster road
Asylum place, William street, Newington Causeway
Asylum terrace, see Kings road, Chelsea
Austin Friars, Old Broad street
Austin Friars passage, Winchester street
Austin street, Shoreditch church
Ave Maria lane, Ludgate hill
Avebury street, New North road
Avery Farm row, Pimlico
Avery row, Lower Grosvenor street, Bond street
Aylesbury place, see Old Kent road
Aylesbury street, Clerkenwell