OP, join your local cycling club and go on some group rides. You'll soon find riders faster than you. Riding with them as much as you can will help increase your average speed. More fun than riding intervals by yourself.

I don't get to ride much except on the weekends and I've hit about the same average as you. I can ride with the "fast" group for a while till they drop me on a climb but that's okay.

Or, you can just buy a new set of carbon tubulars and instantly go 3mph faster!!! Results Guaranteed!!