If you want to take an easy walk - figure 15 minutes. 10 minutes if you walk fast. Maybe 8 if you run. But the corridor has been narrowed in C as you connect to E with bars, shops, etc so you will be dodging people if you walk/run at a pace faster than the flow.
Also many times there are gate changes at the last minute so always check the monitors as soon as you exit (or ask the redcoat). If your C gate were to change to the north section of Term C - then take the overhead train from C to E. But from the south side of Term C - walk.