[The term usually describes universities. A redbrick university is one built
in the UK after WWII, as opposed to the older prestigious institutions such
as Oxford and Cambridge.]e.a.

Having had teachers of German at High School, one with an M.A. (Hons) from Cambridge, the other who seldom missed a chance to deprecate his rebrick alma mater, Reading, I have never heard or read the word used to describe anything other than universities. I could look up the OED but really can't be arsed. Does anybody have citations they've come across that use the word outside the varsity context?