Unions won't pursue Heydon in the courts

Unions won't push ahead through the courts to have royal commissioner Dyson Heydon disqualified.

The man overseeing the inquiry into union corruption rejected an ACTU push for him to stand aside after accepting an invitation to speak at a Liberal Party fundraiser.

ACTU secretary Dave Oliver still wants the commission shut down, but has told the Australian Financial Review "this is a political process, not a legal process and we will treat it as such".