No doubt redbrick can be used literally to mean 'made of red bricks' but I've never seen it used otherwise of anything other than universities.

But, pace Anu, I associate it with universities founded in the late 19th century or early 20th century. There was another round of university expansion in the 1960s but I don't think those universities are usually included in redbrick. As it happens, I've been reading David Lodge's "Changing Places", which was written in 1975 and is set in 1969:

"Rummidge, on the other hand, had never been an institution of more than middling size and reputation, and it had lately suffered the mortifying fate of most English universities of its type (civic redbrick): having competed strenuously for fifty years with two universities chiefly valued for being old, it was, at the moment of drawing level, rudely overtaken in popularity and prestige by a batch of universities chiefly valued for being new."

Bingley