A horse usually “jigs” at the walk when it does not fully accept the rider’s leg. You need to do a lot of relaxing work at the walk, such as riding on trails or in a field, making sure that you don’t take your legs off the horse’s sides for even a moment. If you will concentrate on keeping a light, but steady, feel with your legs, then your horse will learn to expect the constancy of the legs and will even crave it, much like a child craves the comfort of its “security blanket.”
When you are working in the ring, try to keep your horse moving from one bending movement to the next, rather than just going around and around the arena. When working on a bend, you have more control of the horse’s hind legs, particularly the inside hind leg, which is controlled by your inside leg—that is, your leg that is toward the inside of the bend. Movements such as circles, serpentines, half-turns, etc. will slow the horse down a little and tend to make it stay in the four-beat rhythm of the walk, rather than break to the two-beat trot. In addition, using suppling movements, such as the shoulder-in, will help slow your horse and make its footfalls more precise. You can learn how to perform additional lateral movements that can be useful in solving this problem in my latest book, the fourth edition of Judging Hunters and Hunter Seat Equitation.
Finally, half-halts can be beneficial, as long as you keep your legs on all the time, rather than taking them off if the horse breaks gait from the walk to the trot. To learn how to do the half-halt properly, read “How to Perform at Half-halt” in the Horse Articles section of this site. You can go directly there by clicking on http://annamullin.com/how-to-perform-a-half-halt.