When I was an atco at one of the uk's major international airport, the first departure of the day was given taxi clearance, take off clearance and when airborne contact "#####" which the aircraft did without stopping and no further contact. Gone are those days.
On a modern note, unless the pilot is given an "immediate" then in theory the pilot can take as long as required to complete take off checks. If it is a busy airport I will always be ready on reaching the holding point so if an "immediate is required I can accept or if required to hold on the threshold I can comply but as soon as the "cleared take off" instruction is issued we are rolling.