Without knowing what your interests are, I can't really say what you should add or forget. I personally would not pick birmingham or manchester, but you might enjoy them. I do think this itinery does not seem very efficient, at least the Ireland part. You will spend most of one day getting from Dublin to Dingle and then you'll leave the next day for Galway, which is a good half day trip. That's a lot of traveling with no where near enough time to enjoy Dingle, which is absolutely beautiful (my favorite place in Ireland). I hate to say skip Dingle, since I like it so much, but it would make for an easier travel schedule. I also question why you want to tack Edinburgh on at the end. That's going to be another trip across the water. Again I hate to say skip it because it's my favorite city in the world. Could you go there after Manchester?
This trip is more spread out than I think is advisable, but perhaps it will work for you.