A list of pubs which existed in 1961 in London, it confirms their existence, and also their address at the time and you can follow their history on the pubwiki.
Finboro Arms, 118 Finborough Road SW10
Finish, 142 Lynton Road SE1
Finsbury Park Hotel, 336 Green Lanes N4
Finsbury Park Tavern, 263 Seven Sisters Road N4
Fir Trees, 142 Hermon hill E18
Fish & Ring, 141a White Horse Road E1
Fishmongers Arms, 225 St Johns Hill SW11
Fishmongers Arms, Winchmore hill road N14
Fishmongers Arms Hotel, 287 High road, Wood green N22
Fitzroy Arms, 21 Clipstone Street W1
Fitzroy Tavern, 16 Charlotte Street W1 & 43 Windmill Street W1
Five Bells, 153 & 155 New Cross Road SE14
Five Bells, 535 Old Ford Road E3
Five Bells & Blade Bone, 27 Three Colt Street E14
Flask Tavern. 14 Flask walk NW3
Flask Tavern, 77 Highgate West Hill N6
Fleece, 160 Abbey Street SE1
Fleet Tavern, 90 Parkhill Road NW3
Flora Hotel, 525 Harrow Road W10
Florence, 50 Florence Street N1
Florfield Arms, 40 Florfield road E8
Florists Arms, 255 Globe road E2
Flower of the Forest, 123 Blackfriars Road SE1
Flower of Kent, 135 Lewisham Way SE14
Flower Pot, 43 Old Bethnal green road E2
Flower Pot, 19 St Anns Road N15
Flower Pot, 128 Wood street E17
Flying Dutchman, 156-158 Wells way SE5
Flying Horse, 52 Wilson Street EC2
Flying Scud, 137 Hackney road E2
Flying Scud, 76 Rathbone street E16
Flying Wheel, 75 St Pauls churchyard EC4
Fonthill Tavern, 127 Fonthill road N4
Forest Gate Hotel, 105 Godwin Road E7
Forest Glen, 39 Dames Road E7
Forest Hill Hotel, 41 Stanstead Road SE23
Forest Hill Tavern, 108 Forest Hill Road SE22
Forester, 108 Allfarthing lane SW18
Forester, 2 Leighton road W13
Foresters, 19 Rhodeswell road E14
Foresters Arms, 45 Camberwell green SE5
Foresters Arms, 113 Homerton High street E9
Foresters Arms, 27 Lordship lane SE22
Foresters Arms, 76 Mitcham road SW17
Foresters Arms, 182 Peckham High street SE15
Foresters Arms, 86-88 Point Pleasant SW18
Foresters Arms, 253 St Leonards Road E14
Foresters Arms, 78 Southern Row W10
Foresters Arms, 49 Waddington road E15
Foresters Arms, 9 Whitwell Road E13
Foresters Tavern, 53 Perry Vale SE23
Fort Tavern, 26 Sandy Hill Road SE18
Fortune of War, 40 Woolwich New Road SE18
Fortune of War, 184 York Way N7
Founders Arms, 56 Hopton Street SE1
Fountain, 68 Amwell Street EC1
Fountain, 43 Camberwell Road SE5
Fountain, 36 Deptford Broadway SE8
Fountain, 862 Garratt Lane SW11
Fountain, 16 Gillingham Street SW1
Fountain, 211 Lower Clapton Road E5
Fountain, 436a Mile End Road E1
Fountain, 132 Plumstead Road SE18
Fountain, 74 St Georges Road SE1
Fountain, 123 Sceptre Road E2
Fountain, 51 Sewardstone road E4
Fountain, 125 West Green Road N15
Fountain & Star, 31 & 32 Coleman Street EC2
Fountain & Star, 16 Mumford Court EC2
Fountain Abbey, 109 & 111 Praed Street WC2
Four Sisters, 25 Canonbury lane N1
Fox, 56 Ashbrook road N19
Fox, Green lane W7
Fox, 413 Green lanes N13
Fox, 372 Kingsland Road E8
Fox, 62 New Cross road SE14
Fox, 28 Paul Street EC2
Fox, 384 & 296 West Green Road N15
Fox & Anchor, 115 Charterhouse street EC1
Fox & Goose, Hanger lane W5
Fox & Grapes, Camp road SW19
Fox & Hounds, 60 Besson street SE14
Fox & Hounds, 178 Forest lane E7
Fox & Hounds, 492 Hornsey road N19
Fox & Hounds, 150 Kirkdale SE26
Fox & Hounds, 66 Latchmere Road SW11
Fox & Hounds, 29 Passmore road SW1
Fox & Hounds, 57 Plumstead Common Road SE18
Fox & Hounds, 56 Royal Hill SE10
Fox & Hounds, Sewadstone road E4
Fox on the Hill, Champion hill SE5
Fox Tavern, 1 Islington Green N1
Fox under the Hill, 286 Shooters Hill Road SE18
Foxley Tavern, 1 Treherne Road SW9
Frampton Arms, 65 Well Street E9
Franchise, 90 Andover Road N7
Frankfort Arms, 518 Harrow Road W9
Freemasons Arms, 17 Courland Grove SW8
Freemasons Arms, 32 Downshire Hill NW3
Freemasons Arms, 35 Frederick Place SE18
Freemasons Arms, 38 Ladywell Road SE13
Freemasons Arms, 81 & 82 Longacre WC2
Freemasons Arms, 96 & 98 Salmon Lane E14
Freemasons Arms, 1 Spicer street SW11
Freemasons Hotel, Wandsworth Common SW18
Freemasons Tavern, 37 Gilden Road NW5
Freemasons Tavern, 61 Howard Road N16
Freemasons Tavern, 646 Lordship lane N22
Freemasons Tavern, Penge road SE25
Freemasons Tavern, 342 Romford Road E7
Freemasons Tavern, Victoria Dock Road E16
French Horn, 49 Lambeth Walk SE11
French Horn & Half Moon, 37 East Hill SW18
Friend at Hand, 4 Herbrand Street WC1
Frying Pan, 13 Brick Lane E1