High intensity interval training would help.
I'd recommend doing a thing called fartlek running for 20 - 30 mins, 3 - 4 times a week.
After warming up, start by jogging 100m, then sprint for 50m, jog 100m, sprint 50, jog 100m... etc. Be warned, this is a gruelling workout but it will increase your speed tenfold. You should also try working on increasing your time for 50/100m sprints.
Another thing you could try is skipping (jump rope) at a fast pace for as long as you can and gradually increasing the duration as well as trying new things such as double-jumps.
Also, boxing/shadow boxing will increase your upper body speed.