All London's motorways M1: The M1 is the oldest motorway in London but not London's oldest motorway. When the M1 opened on 2nd November 1959 the southern end was J5 at Watford (which is not in London). In 1966 the first extension reached J4 to the south of Elstree (which was marginally in London). In 1968 the second extension reached J2 at Mill Hill (which is definitely in London). In 1977 the final extension reached J1 at Staples Corner, a contorted junction with the North Circular. There had originally been plans for the M1 to reach Marble Arch but thankfully they were binned at an early stage.
Traffic joining the M1 in London cannot exit the motorway before J5 at Watford. J2 only allows northbound traffic in and southbound traffic out (to the A1). J4 only allows northbound traffic in and southbound traffic out (to the A41). There never was a J3 because the proposed connection to the A1 at Stirling Corner was cancelled, so the spur roads here now only provide access to Scratchwood services. People still call it that even though it was renamed London Gateway services in 1998. The guns on HMS Belfast are deliberately trained on Scratchwood Services, so it's just as well they can no longer fire.
M2: The M2 does not enter London, it starts 10 miles outside.
M3: The M3 does not enter London but blimey it gets close. The A316 comes swooshing down past Kempton Steam Museum, crosses the Surrey boundary and just 500m later the dual carriageway morphs into a motorway at Sunbury Cross. M4: The M4 starts at the Chiswick flyover, which was opened in 1959 by the Hollywood actress Jayne Mansfield. A 1½ mile elevated section continues above the original A4 running to the north of Brentford, and this became the A4(M) in 1961. The new motorway later continued across the Brent valley on concrete stilts, descended round the edge of Osterley Park and drove on west past Heathrow. At Slough it joined an existing section of motorway, formally becoming the M4 on 24th March 1965. This was one week before the county of Middlesex disappeared, hence the M4 became Greater London's first motorway on 1st April.
Heston service station has two disjoint halves and is located close to J3. The westbound side opened on 4th March 1967 and the eastern side on 3rd January 1968. J4 is for the spur to Heathrow Airport, which is also designated the M4 and which also opened on 24th March 1965. Originally the next junction was outside London but construction of the M25 demanded a new stacked connection designated J4B. The Thorney Interchange opened on 19th December 1985 and is now Britain's busiest motorway junction. Traffic on the M4 exits London as the motorway crosses the Bigley Ditch.
M5/M6: The M5 and M6 do not enter London.
M7: There is no M7.
M8/M9: The M8 and M9 do not enter London.
M10: The M10 no longer exists, and never entered London anyway. M11: The M11 connects London to Cambridge and was opened in stages between 1975 and 1980, the southern end in 1977. Only two miles of the motorway are inside Greater London, much of this formed of slip roads from the North Circular. It had originally been planned to continue the M11 as far as Islington as part of the GLC's misguided Ringways plan but that all fell apart, much to inner London's great relief. The junction at South Woodford was numbered 4 just in case 3, 2 and 1 were ever built.
M12: The M12 would also have started at South Woodford, heading east to Brentwood to act as a much-needed bypass for the A12 Eastern Avenue. It was never built, although the M11 still rises up so the non-existent M12 could pass underneath. Had it not fallen foul of a GLC change of administration it could have been a mighty useful connection.
M15: The M15 would also have started at South Woodford and was pencilled in to head south towards Beckton. The road was indeed built but not fully to motorway standard and is now part of the North Circular, i.e. the A406. M20/M23/M26: The M20, M23 and M26 do not enter London, but both start less than two miles outside so nearly do.M25: The M25 is London's orbital motorway, running 117 miles in an almost-loop broken only at the Dartford Crossing. It comprises parts of Ringway 3 and Ringway 4, a more comprehensive 1960s project that was never completed. The northern half was originally going to be called the M16. The first section to open was between South Mimms (J23) and Potters Bar (J24) in September 1975, though not yet designated a motorway. The M25 loop was completed when Margaret Thatcher cut a ribbon near South Mimms in October 1986, telling pessimists not to carp and criticise. Only three sections of the motorway are actually in Greater London, all on the boundary: west near Heathrow (J14-J15), north round Enfield (J24-J25) and east past Brentwood (J28-J29). North Ockendon is the only settlement in London to lie outside the M25. Congestion has seen much of the motorway widened to four lanes. M40: The M40 does not enter London but blimey it gets close, starting just quarter of a mile into Buckinghamshire at the Denham roundabout.
A40(M): The Westway was one of the most unpopular roads ever to be built in Britain, carving an eight-lane concrete viaduct through the terraces of Paddington and North Kensington. Demolition and construction took most of the 1960s, the road eventually opening on 28th July 1970 as the A40(M). The furious public reaction to its creation effectively killed off most of the urban motorways then being planned. It remained a motorway for three decades until May 2000 when all main roads in the capital were transferred to a new body called Transport for London. However TfL had no legislative power to be the authority in charge of motorways so the road had to become the plain A40, which it still is. M41: The tiny M41 was built by the GLC as part of their Ringway 1 project. This invasive inner loop would have demolished a swathe of inner London and got built here because not much needed to be demolished. Opened in 1970, the M41 connected the Westway at Ladbroke Grove to the Holland Park roundabout and was just three-quarters of a mile long. But it too fell foul of the transfer to TfL and is now the plain A3220. Cyclists remain prohibited from using it.A102(M): Also part of the planned London Motorway Box, this 1½ mile dual carriageway connected Hackney Wick to the Bow Roundabout. This East Cross Route was intended to funnel traffic from the M11 towards the Blackwall Tunnel, but the M11 never got this far and so only the eastern edge of Bow ended up multiply-demolished to create the new A102(M). South of the river a separate section of the A102(M) sliced through Blackheath ending at the Sun-in-the-Sands roundabout on Shooters Hill Road, and this was opened on 25 April 1969. Both were declassified due to the aforementioned TfL administrative issue, becoming part of the A12 and A102 respectively.
That's the 1200-word version anyway. See Roads.org.uk, Pathetic Motorways, Sabre and Wikipedia for far far more detail.