Have Up Meaning

(transitive, idiomatic, Britain) To accuse, arrest, try for a criminal act.

Example: 2007, Saturday October 27, Don't write off religion - it can be the key to a stable family, by Anne Karpf in The Guardian
  If Richard Dawkins had his way, a fair number of you and, as it happens, me, would be had up for child abuse. According to him, that's what religious indoctrination of children by their parents is.