I have an English Bulldog too, but she is the most dependable of our dogs (other is a Boston Terrier) around the chickens. You have to work with them. Yes, they are super bull-headed, but my Aunt Clara is proof they are capable. She is super dog aggressive, sometimes even to the dogs she lives with.
Here's what we did when we started chickening....
We raised the chicks in the master whirlpool tub, which meant Aunt Clara could hear them and not get to them since the master bedroom is also her lair. I would take the babies out, one at a time and cage them inside my hands at first to let her sniff them and tell her "my chicken," eventually opening my hands and allowing her to inspect them a little more closely. They were usually wet when they went back in the tub (diggy slobber). Once they moved outside, I took her out on a leash and sat inside the run with them. If she acted like she was interested (and she did lunge a time or two), I corrected her by jerking back on the lead and telling her "No! My chicken!" Eventually she did learn to ignore them, and I began dropping the leash but being close enough to grab it if I needed to. And, of course, we eventually got to the point of not needing the leash.
When the chicks began being allowed out of the run to range, I began all over again with the leash in the yard. She learned to accept them as a part of the scenery.
That was three years ago. Now, when I go out to check on them on the mornings and to tick them on and count them at night, I tell her, "Let's go check the chickens," and she happily tags along, eating nothing in the pen except the chicken feed. In fact, she is so good with the chickens that I often leave her outside to watch the yard when they are free ranging because she has been exposed and taught what is expected of her. It takes time and effort.
Now, the Boston Terrier was much more of a challenge, believe it or not (being a terrier), and I would never leave her alone with chicks. We trained her the same way, but her prey drive is much, much stronger. She is super intelligent and obedient, but I do not trust that she would be able to help herself if I wasn't around. However, as long as I am present, I can call her name and she will literally snap her head away from her target. When we got our first babies, she would sit outside the fence and just tremble to get at them. Of course, I would correct her when she did this. It took her awhile to be able to ignore, and now she can be around the free ranging birds too, but I am careful not to put her in a situation where she is confined with birds without supervision. I am certain this is as good as it's going to get for her terrier abilities. I am happy with where we are today with both Zelda and Aunt Clara.
Ultimately, you will reap on your training investment. Also, you have to know your dog's limitations and have realistic expectations. You can definitely get to a good place with this. Just be consistent.
