To go faster on any terrain you either need to turn the pedals faster in your usual gear for it, or keep turning the pedals the same in a higher gear. The latter is more force per pedal stroke.
To turn the pedals faster try doing 30 second efforts on a section of road with no junctions, lights, roundabouts etc. Gradually increase the time you spend spinning the pedals faster.
To push a higher gear at the same cadence you'll want to have stronger legs. You can try same approach as for spinning faster. Drop into a higher gear and try and maintain the same cadence for 30 seconds. Gradually increase the time you spend pushing a higher gear.
If you can't reliably measure cadence during these efforts then use speed as a proxy. So you might try riding 1 or 2mph faster than you typical speed during 30 second these efforts.
You might want to try it fartlek style rather than intervals picking suitable landmarks on the road for such speed play.