Firstly, you've already got an OK pace for a "non runner" so you're looking good to start. As above, intervals is your friend for getting faster, as part of a balanced plan with 3-4 runs/week. There seems to be a lot of buzz around 30-20-10 right now, which has helped me take a minute or so off my 10km time. Adjust the overall times and speeds below, but try something like...
5:00 minute warm up at 12 kph
5x (0:30 at 11 kph, 0:20 at 14 kph. 0:10 at 18 kph)
2:00 recovery at 12 kph
Repeat 5x and recovery two-three-whatever more times
5:00 minute cool down at 12 kph
Like I say, adjust the speed and repeats as needed for you. I do this run once a week, as part of a plan, and cover about 11km in a 50 minute session. I've just run a 1:37 half marathon as a guide.
Google it for more info as to the particular (supposed) benefits.