There is no tag for English literature or Old English literature. If the former will not be added because it would fit most questions on this site, I'd propose the latter be added, as a tag limited in scope but also useful.
I think an old-english tag would definitely be useful. I think a middle-english tag would also be useful, for works such as The Canterbury Tales. There is specific expertise involved in questions about both variants, so a tag would be useful.
However, Old English and Middle English aren't separate languages, they're versions of English. So in this case I would not follow the [language-X-literature] naming convention, which is used for questions that are about non-English works, so as to make this distinction clear. I.e. use old-english, not old-english-literature.