A defection from Australia's most prominent right-wing political party, Pauline Hanson's One Nation, on Thursday robbed it of its ability to block Prime Minister Malcolm Turnbull's legislation, raising the prospect he can introduce tax cuts.

Brian Burston, who will now sit in the upper house Senate as an independent, resigned from One Nation over infighting, the latest blow to the party that re-emerged as a force in Australian politics in 2016.

Turnbull had often needed the support of One Nation to get legislation passed although the third-largest party in the Senate had recently blocked plans for corporate tax cuts, and threatened to block income tax cuts.