This would be London City Airport, which is located in the eastern suburbs of the city not far away from The Docklands (the new skyscraper district).
However, this airport is restricted to mainly business and charter flights. So you're more likely to end up at Heathrow Airport, which is the second closest.
Don't be too worried about distance though, as all airports are well connected to London. I'd rather take flights to Stansted Airport (which is quieter than Heathrow but much further away) than Heathrow (which is very busy).
London City Airport is closest but it is very small and flights are limited. Heathrow and Gatwick are the busiest airports and central London is easily accessible from both.
London City Airport.
London Heathrow Airport is nearest airport to Hayes in London
London City Airport is very close to Central London. However, the number of destinations from there is limited. Heathrow and Gatwick are the two main London Airports and are both about 30 miles from Central London and easily accessible. Heathrow lies to the West of London and Gatwick to the South.
The closest commercial airport to Chicago Union Station is Midway Airport.
London City airport is nearest to the US embassy in London.
The nearest airport to the London Olympic stadium is the London City Airport in east London.
London City is the closest (in a straight line)
The closest international airport is Lindbergh Field (near downtown San Diego)
Heathrow
Slough is closest to Heathrow airport in London.
"There is a Travelodge located approximately nine miles from downtown London, UK. It is located at the London City Airport and near the Woolwich Ferry."
Heathrow