I usually run a 6min mile on grass track, so no idea how much faster it would be on a decent surface.
My advice for decreasing your mile time is to work on intervals of different lengths. I use the following two to get my times down (and to make my cardio hurt like hell):
3min fast run/1min rest x 6
1min fast run/1min rest x 10
These are maximum effort runs, so you should be feeling the pain in the early reps and not leaving something in reserve for the later reps. If you're not crawling home near the end then you need to be moving faster.
Stick with something similar to these (and the occasional longer run) for a while and you'll be in a good position to improve your times.
My advice for decreasing your mile time is to work on intervals of different lengths. I use the following two to get my times down (and to make my cardio hurt like hell):
3min fast run/1min rest x 6
1min fast run/1min rest x 10
These are maximum effort runs, so you should be feeling the pain in the early reps and not leaving something in reserve for the later reps. If you're not crawling home near the end then you need to be moving faster.
Stick with something similar to these (and the occasional longer run) for a while and you'll be in a good position to improve your times.