The prudential watchdog is formally investigating industry superannuation funds’ payments to unions and whether these meet trustees’ ultimate legal duty to act in members’ best financial interests.

The investigation comes as Labor’s critics suggest that the hefty payments unions receive from industry super funds annually and Treasurer Jim Chalmers’ eagerness to tap the funds’ $3.5 trillion retirement savings pool for “nation-building” investments gives industry super an outsized influence in Canberra.