Heathrow airport (LHR) is the closest. Distance: 18 miles/29KMs. A taxi will take 1 hour at a charge of around £65.00 one way.
You can also take the Piccadilly Line tube from Terminals 1,2,3, 4 or 5 direct to King's Cross St. Pancras station. Alternatively take the Heathrow Express to Paddington station and change for the Circle Line to King's Cross station. When you arrive at the station follow directions above.
For further information: Transport for London - Journey Planner