I agree with Sharpie, the walking speed is more often due to training. I train all my horses to really reach out and walk though even with that, some are able to walk faster than others.
What I do is to gently urge them with my legs to go faster without actually asking for a gait transition. If they pick up a trot, then I immediately slow them back to a walk and then immediately start urging again. When they start to pick up a faster walk without acting like they want to change gaits, then I let my legs off and let them go along on their own for as long as they'll keep the pace. If they start slacking off, then I start urging again. It takes lots of time and they need to build up their stamina to be able to maintain that fast walk, but it works.