Former Liberal senator Cory Bernardi has pointed the finger at Malcolm Turnbull as the government accuses Labor of conspiring with a foreign political party.

Senator Bernardi helped deliver an embarrassing parliamentary defeat for the coalition on Wednesday when he voted with Labor and the Greens to thwart a censure move against Labor frontbencher Penny Wong.

Senator Wong has admitted her chief of staff was involved in fishing for information during a conversation with a friend from the NZ Labour Party - something she has since labelled unwise - that contributed to Deputy Prime Minister Barnaby Joyce's eligibility to sit in parliament being referred to the High Court.

Fresh from the vote, Senator Bernardi revealed the prime minister and others contacted someone in the UK Tory party and tried to stop him speaking at one of their conferences.

"No one here is without sin," he told Sky News.

"They would all exploit the same opportunity."

Senator Bernardi accused the government of overcooking the allegations of conspiracy.