The nearest airport is in Heathrow Airport (LHR), located 11.9 mi (19.1 km) from the city centre. If you're unable to find a flight that fits your schedule, you might consider flying into London (LCY-London City), which is 10.8 mi (17.4 km) away.
Consider catching a ride on the metro at London Kilburn High Road Station or Kilburn Park Underground Station and easily see more of the city.