As the citizenship crisis engulfing the Federal Parliament deepens, and coming just a day after Deputy Prime Minister Barnaby Joyce announced he was a dual national of Australia and New Zealand, Fairfax Media has confirmed that Ms Sudmalis has been in contact with the British government to clarify her status.

Ms Sudmalis, the member for Gilmore in NSW, is one of a number of MPs facing questions about her citizenship by descent with a foreign country, following the revelation that Mr Joyce was automatically granted New Zealand citizenship.

In turn the government has turned its sights on Labor, demanding the opposition provide documentation for four of its MPs - Tony Zappia, Maria Vamvakinou, Justine Keay and Susan Lamb.

Ms Sudmalis was born in Australia in 1955, to an Australian father and a British mother. Her mother, Valerie Pybus, came to Australia in 1951 and did not become an Australian citizen - and renounce her British citizenship - until 1989.

Ms Sudmalis, elected to Federal Parliament in 2013, has never taken up British citizenship but nor has she renounced her entitlement to it.

According to the British Home Office guidelines on citizenship, a person is entitled to register for citizenship through their mother if they were born before January 1, 1983; they would have become a citizen of the United Kingdom and Colonies by descent if women had been able to pass on citizenship to their children in the same way as men at the time of their birth; and they have right of abode which they acquired because their mother was, at the time of their birth, a citizen of the United Kingdom and Colonies.

A person must also be of good character in the view of the British Secretary of State.

Ms Sudmalis appears to have satisfied all of these criteria. She may also face difficulties under section 44, part (i) of the constitution.

That section states that a person is disqualified from standing for Parliament if they are "under any acknowledgment of allegiance, obedience, or adherence to a foreign power, or is a subject or a citizen or entitled to the rights or privileges of a subject or a citizen of a foreign power".

Constitutional scholar George Williams told Fairfax Media that Ms Sudmalis' case could also hinge on whether citizenship was automatically conferred on her, or whether she had applied for it.

This, he said, "depended on UK law and whether that nation regards her as a citizen".

"No one is certain about how broad ranging the definition of entitlement might be," Professor Williams said. "If it means what it suggests, what we have seen so far for section 44 is really just the tip of the iceberg because it would cover anyone who might be eligible to apply for citizenship."

Labor manager of opposition business Tony Burke flagged on ABC radio on Tuesday morning that Ms Sudmalis may have an issue regarding her status.

"When Christopher Pyne yesterday in the Parliament started throwing accusations across the chamber, you could see sitting behind him in the camera shot the members for Gilmore [Ms Sudmalis] and the member for Chisholm [Julia Banks] and the colour draining away from their faces. I presume that the process [the vetting process Labor undertakes on candidates] that I've just described for the Labor Party are not processes that the Liberal Party, the National Party, the Greens or One Nation have," he said.

Ms Banks declared last month that she was in the clear and not a dual Greek-Australian citizen.

A spokeswoman for the British high commission said "we can't comment on individual cases, nor can we speculate on who may be entitled to British citizenship".

Ms Sudmalis declined to comment.

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