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Take Northern Line northbound to Leicester Square, then change for the Piccadilly Line northbound to get to King's Cross St. Pancras. I recomend that a change at Leicester Square is easier than at Euston.
The Northern Line (Black one)
As there are no direct trains from Heathrow to London Waterloo, it's quicker to travel by underground from Heathrow on the Piccadilly Line to Leicester Square Underground Station and then change onto the Northern Line to London Waterloo Railway Station.
Take the Piccadilly line from Heathrow to King's Cross St Pancras (St Pancras is the Eurostar station).
The most direct path is east to the A201 south, across the Blackfriars Bridge to Southwark and then "The Cut" west to Waterloo Road. It is 6 minutes faster, on average, to use the A4200 due south across the Waterloo Bridge.
Take the Piccadilly underground (tube) line directly to St Pancras from all terminals at Heathrow.
The journey time at morning peak is between 25 and 30 minutes, dependant on whether or not you are prepared to change train enroute.
From Waterloo take the Bakerloo line to Oxford Circus. There transfer to the Victoria line to St. Pancras International rail station. Journey takes about 20 minutes with one change of train. Check the 'London Tube' site for service delays and restrictions.
It's complicated as there are no direct trains. Your best bet would be to take a train to Waterloo and then transfer on to the Underground.
couple of hours (3?) if you take the high speed to st pancras
About 1 hour.
Go to Google Maps.