I ask restaurants to hold the Black Pudding because I don’t enjoy it, I don’t need calories from foods I don’t enjoy, less waste and more for somebody who enjoys it.
I don’t eat things I don’t like to be authentic. I like the rest of the English breakfast.
Also, vegetarian Full English breakfasts are found all over the place in the UK, and they never have black pudding. I don’t think it’s necessary for a breakfast to have Black Pudding for it to be called an a Full English breakfast just because it’s traditionally part of one.