jno, it is possible to have a duplicate name, where there is both a Church of England and Roman Catholic cathedral. Newcastle and Portsmouth spring to mind, and most famously, Liverpool. (If you want a cathedral, we've got one to spare was the Liverpudlians’ boast).
There's no point calling Westminster Abbey a "cathedral", as there is no bishop's throne there, which is the requirement in CoE terminology. (I believe it has a status by which it does not fall under the jurisdiction of any bishop.)