We are staying in the Earl's Court area and are hoping to use that tube station to get to St. Pancras/King's Cross. We have eurostar tickets that depart from St. Pancras at 6:55 am (to Paris). I know we need to check in at least a half hour before we leave. My question: Does the tube run early enough to get us from Earl's Court to St. Pancras by 6 am or shortly after? How much time should we allow to do this? Any tips to make this go smoothly?