South-Eastern high speed service from Stratford International to St.Pancras in about 7 minutes (Note that Stratford International is a separate station, not accessible except by means of a short bus or DLR link from the main station)
London Overground Train Stratford to Caledonian Road and Barnsbury, then 10 minute walk or any bus to King's Cross.
Alternatively, any train or Central line Underground to Liverpool Street, then circle, Metropolitan, or Hammersmith and City line line