I think that you're covering the right distance to do a 10K and that you just need to try and run for a longer period of time without stopping, You don't say how often you are going out for a run. My advice would be to go out at least three times a week and try and cut out some of the time spent walking. You could also mix it up a bit by replacing one of your sessions with two miles of hills to build up some more endurance. It might also be worth getting involved in one of the wekly parruns, which are a times 5k race.
Try up and running. They should have a treadmill instore and will be able to look at your running style so you can find the right shoe. http://www.upandrunning.co.uk/shops.html.
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Matthew Wild 2
