Not many people know this, but...
Most people who live in London assume the postcodes are numbered according to their distance from the centre of London. This is often borne out by the evidence - SW19 is indeed further than SW3. But W3 (Acton) is miles away; and I'd far rather walk to N7 than N2 (East Finchley).

This is how it works: they're alphabetical. In each sector, the postal district nearest the centre of London is given the number 1. Then they are numbered in more-or-less alphabetical order, as follows:

North

N1 Canonbury and Islington

N2 East Finchley

N3 Finchley

N4 Finsbury Park, Haringay

N5 Highbury

N6 Highgate

N7 Holloway

N8 Hornsey

N9 Lower Edmonton

N10 Muswell Hill

N11 New Southgate

N12 North Finchley

N13 Palmers Green

N14 Southgate

N15 South Tottenham

N16 Stoke Newington

N17 Tottenham

N18 Upper Edmonton

N19 Upper Holloway

N20 Whetstone

N21 Winchmore Hill

N22 Wood Green

East

E1 Aldgate East, Shoreditch, Stepney, Wapping and Whitechapel

E2 Bethnal Green

E3 Bow

E4 Chingford

E5 Clapton

E6 East Ham

E7 Forest Gate

E8 Dalston and Hackney

E9 Homerton

E10 Leyton

E11 Leytonstone and Wanstead

E12 Manor Park

E13 Plaistow

E14 Poplar

E15 Stratford

E16 North Woolwich and Victoria Docks

E17 Walthamstow

E18 South Woodford

E20 Walford (!)

South-East

SE1 Bermondsey, Lambeth (North), Waterloo

SE2 Abbeywood

SE3 Blackheath and Lee Green

SE4 Brockley

SE5 Camberwell

SE6 Catford

SE7 Charlton

SE8 Deptford

SE9 Eltham

SE10 Greenwich

SE11 Kennington

SE12 Lee

SE13 Lewisham

SE14 Newcross

SE15 Peckham

SE16 Rotherhithe

SE17 Walworth

SE18 Woolwich

SE19 Norwood

SE20 Anerley, Penge

SE21 Dulwich

SE22 East Dulwich

SE23 Forest Hill

SE24 Herne Hill

SE25 South Norwood

SE26 Sydenham

SE27 West Norwood

SE28 Thamesmead

South-West

SW1 Belgravia, Knightsbridge, Victoria and Westminster

SW2 Brixton (South) and Streatham (North)

SW3 Chelsea

SW4 Clapham

SW5 Earls Court

SW6 Fulham

SW7 South Kensington

SW8 Lambeth (South)

SW9 Brixton (North) and Stockwell

SW10 West Bromton

SW11 Battersea

SW12 Balham

SW13 Barnes

SW14 Mortlake

SW15 Putney and Roehampton

SW16 Norbury and Streatham (South)

SW17 Wandsworth Common, Tooting

SW18 Wandsworth

SW19 Merton, Wimbledon

SW20 Raynes Park

West

W1 Marble Arch, Marylebone, Mayfair, a bit of Euston

W2 Paddington

W3 Acton

W4 Chiswick

W5 Ealing

W6 Hammersmith

W7 Hanwell

W8 Kensington

W9 Maida Vale

W10 Kensington (North)

W11 Notting Hill

W12 Shepherds Bush

W13 West Ealing

W14 West Kensington

North-West

NW1 Camden, Euston, Regents Park

NW2 Cricklewood

NW3 Hampstead and Swiss Cottage

NW4 Hendon

NW5 Kentish Town

NW6 Kilburn, West Hampstead

NW7 Mill Hill

NW8 St Johns Wood

NW9 Kingsbury and the Hyde

NW10 Harlseden, Kensal Rise, Neasden, Willesden

NW11 Golders Green

East-Central

EC1 Clerkenwell and Smithfield

EC2 Bishopsgate and Moorgate

EC3 Aldgate, Bank and Billingsgate

EC4 Cannon St, Fleet St, Farringdon St area

West-Central

WC1 Kings Cross and Holborn (North)

WC2 Holborn (South), Covent Garden and Trafalgar Square