To improve your fitness levels you have to push your cardiovascular system, this is what makes you feel like you are dying from lack of oxygen and your muscles are killing (oxygen transportation system in basic terms). Best way I found to do this is train at least 3-4 times a week, obviously your test is on a treadmill; so train as much as possible on one.
First of all lets do some maths, you need to be running at a minimum of 11 km/h to scrape the bottom of the barrel, this is a risk. I would say an ideal slowest speed would be 12 km/h this should give you a nice finishing time of just over 12 minutes ish. Plenty of time to recover if not all goes to plan.
When I was training I did a timed run at the begging of every week to act as a compass of improvement. The the rest of my training days I would do mainly high intensity training, as this is really what the test is. Best thing to do to improve quickly is interval training, very quick runs for roughly a minute, then give you self 30-60 secs recovery at moderate/recovery pace (Try and avoid cheating on this recovery time as it will only dampen your improvement). Continue to do this as many times as possible, preferably around 15 - 20 mins worth of running each session.
Also at least one session a week for muscles strengthening, (swimming and cycling are great for this) you'll be surprised how much this helps. Remember if you train harder you'll find the test easier, realistically when training you want to be pushing past that 12km/h, mainly seeking 13-14km/h (closer to what males have to run, as this will also make Halton easier if you pass).
Incline as a minimum of level 1.0 on a treadmill must in training, preferably more (do no use on the weekly timed run, as it will effect you run and it is not present on your actual test). This will increase muscle strength, and fitness level. But it also is great for keeping away shin splints what are very common in treadmill work.
NorthFace