In that direction (Euston to St Pancras), it's almost not worth getting on your bike. Just walk along the extremely crowded pavement of Euston Road. But the eastbound road is even busier, with three lanes of $any_vehicle, and a left-hand lane for buses and taxis.
I'm assuming you're using South Eastern Trains "Javelin" service from platforms 11-14 of St Pancras, via the High-Speed-Line to Ashford.