Here's a JSON file of all the inner cities within London. I compiled it when using it for a project.

london_cities.json

["Abbey Wood","Acton","Aldwych","Archway","Barking","Barkingside","Barnes","Battersea","Bayswater","Beckenham","Beckton","Belgravia","Belvedere","Bermondsey","Bethnal Green","Biggin Hill","Blackfen","Blackheath","Bloomsbury","Bounds Green","Bow","Brixton","Brockley","Bromley","Brompton","Burnt Oak","Camberwell","Camden","Carshalton Beeches","Catford","Central London","Chelsea","Chingford","Chislehurst","Chiswick","Clapham","Cockfosters","Colindale","Colliers Wood","Cricklewood","Crouch End","Croydon","Crystal Palace","Deptford","Docklands","Ealing","East Dulwich","Edmonton","Elephant & Castle","Eltham","Erith","Euston","Finchley","Finsbury Park","Forest Hill","Fulham","Golders Green","Greenwich","Hackney","Hammersmith","Hampstead","Harlesden","Harold Hill","Harringay","Heathrow Airport","Hendon","Herne Hill","Heston","Highbury","Highgate","Holloway","Honor Oak Park","Hook","Hornchurch","Hornsey","Ickenham","Islington","Kennington","Kensal Rise","Kensington","Kentish Town","Kidbrooke","Kilburn","Lee","Lewisham","Leytonstone","Maida Vale","Manor Park","Mill Hill","Mitcham","Mornington Crescent","Muswell Hill","Neasden","New Cross","New Malden","Norbury","Northolt","Notting Hill Gate","Orpington","Palmers Green","Peckham","Penge","Petts Wood","Plumstead","Pratt's Bottom","Primrose Hill","Putney","Richmond","Romford","Rotherhithe","Royal Oak","Ruislip","Shepherds Bush","Shoreditch","Sidcup","South Bank","Southall","Southwark","Spitalfields","St Johns Wood","Stanmore","Stockwell","Stoke Newington","Stratford","Streatham","Thamesmead","Tooting","Tottenham","Tottenham Court Road","Tufnell Park","Tulse Hill","Turnpike Lane","Upminster","Vauxhall","Walford","Waltham Cross","Walthamstow","Wanstead","Waterloo","West Hampstead","Westbourne Park","Whitechapel","Whitton","Wimbledon","Wood Green","Woolwich"]