I had to do something similar a few months ago and also a bleep test to a miniumum of level 10. The thing that worked for me to get much better at short and fast was, well hill sprints 3 x a week aswell as my normal running. I do 8 or 10 x 100 metre hill sprints. Best effort on the uphill and gentle down, then sprint again 8 or 10 times. Really worked for me but does take it out out of ya. Look into doing Tabatta training aswell. Its basically picking some body weight exercises, say burpees, jumping lunges etc, then its 20 secs balls out with an exercise, 10 secs rest then balls out for another 20 secs. Do this until you have completed 8 balls out reps. Your only actually working for 4 minutes, but again, you will be hanging out at the end. This method has been proven to improve VO2 max better than a 40 minute run.
Oh, and try British Military Fitness, if they run classes in a park near you. Its a cracking form of fitness and you'll be getting fitness advice from military PTI's, some of which have been Royal Marine baton swingers.
Good luck.
