Labor is dramatically escalating its pressure on Dyson Hedyon to stand aside as head of the royal commission into trade unions by moving a motion in the Senate calling on him to quit, after Fairfax Media revealed the former High Court judge agreed to address a Liberal Party fundraiser.

Mr Heydon is resisting calls to stand aside, despite admitting to "overlooking" the Liberal Party connection and being sent the fundraising leaflet two months before he cancelled the speaking commitment.

The opposition's leader in the Senate, Penny Wong, gave notice of the motion on Tuesday, with Labor to talk to the crossbench about when the Senate should debate it.