This is the earliest street directory I have found so far which also includes publican detail.
London Street Listings in 1832.
Wakefield street, Regent street, St Pancras
Walbrook buildings, Walbrook
Walbrook row, Hoxton New town
Walcot place, Lambeth
Walnut tree walk, Lambeth
Walsingham place, Kennington road
Walworth place, see Walworth road
Wardour Mews, Soho
Wardour street, Soho
Wardrobe place, Doctors commons
Wardrobe terrace, Doctors commons
Wards row, see Bethnal Green road
Warkworth terrace, see Commercial road
Warner street, New Kent road
Great Warner street, Clerkenwell
Little Warner street, Clerkenwell
Warners yard, see 9 Mincing lane
Warnford court, Throgmorton street
Warren street, Fitzroy square
Warwick court, Holborn
Warwick lane, Newgate street
Warwick place, Bedford row
Warwick row, see Blackfriars road
Warwick square, Newgate street
Warwick street, Charing cross
Warwick street, Golden square
Water lane, Blackfriars
Water lane, Dockhead
Water lane, Fleet street
Water lane, Great Tower street
Water street, Blackfriars
Water street, Strand
Waterloo place, Lambeth
Waterloo place, Pall mall
Waterloo road, Lambeth
Waterloo street, Camberwell
Great Waterloo street, Lambeth
Waterloo street, St Lukes
Waterloo terrace, see Commercial road
Watney street, Commercial road
Watton place, see Blackfriars road
Weavers lane, Tooley street
Webb street, Bermondsey street
Webber row, Blackfriars road
Webber street, Great Surrey street
Weigh house yard, Eastcheap
Well court, Queen street, Cheapside
Well street, Camberwell road
Well street, Cripplegate
Well street, Mile End new town
Well street, Wellclose square
Wellesley street, Chelsea
Wellington place, see Commercial road, Limehouse
Wellington place, see Commercial road, Whitechapel
Wellington place, Goswell road
Wellington place, Great Surrey street
Wellington street, Goswell street
Wellington street, Great Surrey street
Wellington street, Newington causeway
Wellington street, Pentonville
Wellington street, Stoney fields
Wellington street, Strand
Wellington terrace, see Waterloo road
Wells row, see Upper street, Islington
Wells street, Grays Inn road
Wells street, Oxford street
Wells street, St James's
Wells yard, Goodmans fields
Wenlock basin, Regents park - see Regents canal
Wenlock street, St Lukes
Wentworth place, see Mile end road
Wentworth street, Whitechapel
Westbourne place, Pimlico
Westbourne street, Pimlico
West lane, Bermondsey
West place, Bath street, St Lukes
West row, Golden square
West street, Finsbury & Circus
West street, Golden square
West street, Soho
West street, Seven Dials
West street, Spitalfields
West street, West square, Southwark & West square
West street, West Smithfield
West street, Somers town
West street, Walworth road
West Harding street, shoe lane
Westmoreland Buildings, Aldersgate street
Wheatsheaf yard, Farringdon street
Westmoreland place, City road
Westmoreland street, Marylebone
Weston street, Bermondsey
Weymouth mews, Portland place
Weymouth place, see New Kent road
Weymouth street, Portland place
Weymouth terrace, Kingsland road
Wheeler street, Spitalfields
Whiskin street, Clerkenwell
Whitcomb street, Haymarket
White street, Borough
White street, Little Moorfields
Whitecross place, Finsbury
Whitecross street, Cripplegate
Upper Whitecross street, St Lukes
Whitecross street, Borough
White Conduit street, Pentonville
White Conduit terrace, Islington
Whitefriars, Temple
Whitehall, Parliament street
Whitehall yard, Whitehall
White Hart court, Bishopsgate
White Hart court, Lombard street
White Hart place, see Lower Kennington lane
White Hart row, see Grays Inn road
White Hart street, Kennington
White Hart street, see Newgate market
White Hart yard, Brook street, Holborn
White Hart yard, Drury lane
White Horse street, Piccadilly
White Horse lane, Stepney
White Horse street, Stepney
White Horse terrace, White Horse street, Stepney
White Horse yard, Drury lane
White Horse yard, Friday street
White Lion court, Birchin lane
White Lion street, Chelsea
White Lion court, Cornhill
White Lion court, Throgmorton street
White Lion street, Goodmans fields
White Lion street, Pentonville
White Lion street, Spitalfields
Great White Lion street, Seven Dials
Little White Lion street, Seven Dials
White Rose court, Coleman street
White alley, Coleman street
White grounds, Bermondsey
Whitmore place, Hoxton
Whitmore row, Hoxton
Whitmore road, Hoxton
Whites row, Spitalfields
Whittlebury street in 1842
Widegate street, Bishopsgate
Wigmore street, Cavendish square
Great Wild street, Lincolns inn fields
Little Wild street, Lincolns inn
Wilderness lane, Salisbury square
Wilderness row, Clerkenwell
Wilkes street, Spitalfields
William street, Blackfriars road
Williams street, Lant street, Borough
William street, Bridewell precint
William street, Hampstead road
William street, Newington causeway
William street, New cut
William street, Gordon square
William street, Regents park
William street, Manchester square
William street, Shoreditch
William street, Spafields
William street, Whitechapel
Williams court, Great Guildford street, Borough
Williams place, see Walworth road
Willow Walk, Bermondsey
Wilmington square, Spafields
Wilmington street, Spafields
Wilmot square, Bethnal green road
Wilmot street, Bethnal green
Wilmot street, Russell square
Wilson street, Finsbury
Wilson street, Grays inn road
Wilsted street, Somers town
Wilton place, Knightsbridge
Wilton street, Regent street, Westminster
Wimpole street, Cavendish square
Winchester place, see New road, Pentonville
Winchester place, Union street, Borough
Winchester row, see New road, Marylebone
Winchester street, Waterloo town
Great Winchester street, Old Broad street
Winchester street, Pentonville
Little Winchester street, Broad street
Windmill court, Giltspur street
Windmill lane, Camberwell
Windmill place, see Camberwell road
Windmill row, Kennington green
Windmill street, Finsbury
Windmill street, Lambeth
Windmill street, Tottenham court road
Great Windmill street, Haymarket
Little Windmill street, Haymarket
Windsor court, Monkwell street
Windsor street, Bishopsgate
Windsor place, see Old Kent road
Windsor street, Lower street, Islington
Windsor terrace, see City road
Windsor terrace, see Great Dover street
Wine Office court, Fleet street
Wingrove place, Clerkenwell
Winkworth buildings, City road
Winkworth place, City road
Winifred place, Bermondsey
Winsley street, Oxford street
Winstone terrace, see Great Waterloo street
Wittams buildings, see Old Street road
Woburn court, Bloomsbury
Woburn buildings, Tavistock square
Woburn place, Russell square
Upper Woburn place, Tavistock square
Walsingham place, Lambeth
Wood street, Cheapside
Wood street South, King square, St Lukes
Wood street North, King square
Wood street, Westminster
Wych street, Strand
Wyndham street, Bryanston square
Wynyatt street, Goswell road
Wood street, Spafields
Wood street, Spitalfields
Woods mews, Grosvenor square
Woodstock street, Marylebone
Little Woodstock street, Marylebone
Woodstock street, Oxford street
Worcester street, London Docks
Worcester street, Union street, Borough
Wormwood street, Bishopsgate
Worship street, Finsbury
Wych street, Strand