'Black Tie' is something specific ('tuxedo' is an American term). Black Tie means a specific coat, with satin lapels, trousers with a single braid down the outer seam, a fold-down white collar shirt with a marcella or poplin 'bib', black dress studs, black bow tie (never a 'ready-tied' version) and patent black shoes. Variations on this don't exist if you want to do it properly - it is what it is.
All of this is available to hire if you don't currently own it. Alternatively, given that it's UoH, you could substitute a black lounge suit, white fold-down collar shirt (i.e. a 'normal' shirt), black bow tie and black shoes, and probably no-one would notice.