Yeah, you can interchange them. Unless the english bridle is a snaffle bridle with a flash band there's really no difference in the mechanics of either headstall. I think it's the trend right now for western headstalls to have browbands instead of the old one-ear or two-eared bridle. What makes the headstall behave the way it does is the action of the bit. If you put a direct-rein bit in the horse's mouth, there's no pressure on the headstall. But if you use a leverage bit, it pulls down on the poll. So, either way I think the headstalls are interchangeable. (and you can always take the flash band off...I use a low-port Kimberwick and did that when a snaffle bridle was all I had)
Reins are reins. My daughter uses a hot pink nylon set. lol. But like somebody else said, make sure that when you change to english reins or barrel reins that you make sure your hands work the bit the way the bit was designed to be used, regardless of what style the reins themselves are. If it's a snaffle (no shanks) you can use 2 hands, but if the bit has shanks (leverage) you should probably still neckrein.