Improving your speed starts with getting stronger, and to do that you'll need to spend some time in the gym.
The foundation of your strength training should include squats, deadlifts and shoulder presses. After you've developed a solid base, you can add exercises that will help build your top-end speed by increasing your force production. Force production allows you to reduce the amount of energy used while producing the same amount of watts, which will help you to ride farther and faster in all-out efforts.
Do these exercises to increase your acceleration, speed and power on the bike once you've built up a solid foundation in the gym.