Ride with others
You might consider this cheating but riding with other people will increase your average speed in several ways. Firstly if you take it in turns to ride in front and share the work of cutting through the wind you will travel faster as a group than on your own. Riding with others will also encourage you to lift your effort level, trying to keep up with someone a bit faster than you will help increase your average not just on that ride but help build your fitness for future rides.
Pump up your tyres
Correctly inflated tyres will roll faster. You should check your tyre pressure before every ride as changes in temperature and slight seeping of air can mean that they go soft without necessarily being punctured. Check the side-wall of your tyre for the recommended pressure. Invest in a track pump so that you can easily get the pressure you need, a mini-pump is best kept only for emergencies out on the road.