I don't know if anybody mentioned this yet, but you need to do resistance training to increase the force you can exert with your legs. Basically, that's 6-10 reps at the max weight you can manage repeated 3 times. You do this with squats with weights, step-ups with weights, or leg machines at the gym. Remember; no pain, no gain.

Intervals are good, but their purpose is to increase aerobic capacity. They don't necessarily increase muscular strength.