Tiny is right....the horse should be respecting you no matter whether they are next to you are five feet behind. This comes in time, some faster than others. Your job is to keep the body language consistent. As others have said, being random is key too. Whenever I get a new horse, and we are learning that 'fine line' of who is in charge....when going from point A to point B would often change. Meaning....sometimes we would just walk from point A to point B, sometimes we would do a couple circles on our way from point A to point B, sometimes we would take a different route, go around a tree, stop and back up....whatever you want. The purpose is to teach them that they need to focus on you and to always be in the mindset of questioning what you are going to ask of them next.
In the beginning, I would take trail walks with a whip....whatever type makes you the most coordinated with your horse. I have them walk shoulder to shoulder. If they start lagging behind, first they start to feel some tension in the lead line, then they hear me cluck and if they don't speed up they feel the swing of the whip string on their butt. I think it resembles the swish of my tail (me being the alpha horse). I never turn to face them. If they are too far back at that point for my whip to reach them, I will back up a few steps and try again. If they speed up, they first feel the tension in the lead line, then I say my verbal cue (mine is hey, hey, hey) and then if they still don't slow down, I swish the whip in front of their chest and we halt and they back up. Then, when I'm ready we go forward. Depending on the severity of their behavior at that point, I will yield their forequarters away from me, or back up more....just kind of depends on what is going on.
One thing I also ALWAYS do...even nowadays when my horses have wonderful ground manners and listen very well, is make THEM move, not myself. Whether we are walking together, I'm mounting, I'm feeding them....whatever it is.....I make them move out of MY way, not the other way around. For example..if mounting and they move....I move them back to where they should be. I NEVER move the mounting block to meet them or follow them around if mounting from the ground. When going into their paddock with their bowls of feed....I make them move out of my way before I enter the paddock gate. They always keep their distance from me all the way to where I feed them. Sometimes I even play the game of not letting them think that as soon as their food goes down that they can have it....sometimes they have to wait a second until I have everything ready. These games are our regular routine and keeps me in the top pecking order with them.
I hope I explained this ok for you and didn't ramble..lol.
P.S. Horses should NOT be 'scared' of whips or any other equipment used. However, that does not mean that the equipment is not useful or doing it's job. It's all in how you use it.