The federal government's hopes of passing contested legislation in the Senate have been thrown into chaos following explosive revelations that its most compliant crossbench senator, Family First's Bob Day, may not have been legally elected.

Acting on legal advice, the government now believes it has been renting office space on behalf of the senator, whose company actually owned the premises.

That would be a breach of the constitution amounting to a "direct or indirect pecuniary interest" with the Commonwealth – which is specifically prohibited – and enough to make a person receiving such profit ineligible to stand as a member of the Australian Parliament.

The news is set to force a recount of all South Australian Senate votes from the July 2 election, and that in turn could result in the election of another crossbench senator or even one from the opposition – potentially changing the composition of an already hostile upper house.