Take the Bakerloo line to Baker Street, then change to the first available train to King's Cross (Metropolitan, Hammersmith and City, or Circle Line)
An alternative, generally slower route, is to use the Circle or District Line to Edgware Road, then change for King's Cross. This route may be better for anyone with heavy luggage or who cannot walk very far as it involves fewer stairs.
If you arrive on platform 14, or the west end of any of the platforms, make your way to the west end of the station and follow signs to Hammersmith and City Line. There is a separate Underground station from which trains on the Hammersmith and City line and Circle line run frequently, if not always rapidy, direct to King's Cross.
Bus 46 from the west end of the station, stop T, on Bishop's Bridge Road. This route is slow and circuitous, it takes around 55 minutes and the journey time varies according to traffic conditions. This route is only reccommended if you can only use the bus and want to avoid changing bus on the route. Otherwise, take bus 27 from Praed Street to Baker Street then bus 30 or 205 to King's Cross.