British Lamb now 100 per cent Aussie MP

Angus Livingston, AAP Senior Political Writer

Labor's Susan Lamb has finally dumped her British citizenship months after being told it made her ineligible to sit in parliament.

The Brisbane-based Longman MP can now run in her seat's by-election, which can't be held until June 23 at the earliest.

Georgina Downer, the South Australian Liberal candidate for Mayo, also revealed she renounced her British citizenship in September last year.

"Susan Lamb is eligible beyond any doubt to run in the by-election of Longman and she will be an excellent flag-bearer," Labor leader Bill Shorten told reporters in Brisbane on Tuesday.

She faces a tough contest to regain the seat, which she held with a wafer-thin margin of 0.8 per cent.

Ms Lamb was told last year she would likely have to resign, but she held on until last week when the High Court ruled ACT Labor senator Katy Gallagher ineligible due to her British citizenship.

Labor MPs Justine Keay, Josh Wilson and Centre Alliance's Rebekha Sharkie also resigned, while Labor frontbencher Tim Hammond quit for family reasons, triggering a total of five by-elections.

Ms Downer is running in Mayo against Ms Sharkie, after losing several Liberal preselections in Victoria.

"I'd like to be an example to people that you can come back and have a fantastic life here," Ms Downer told reporters.

Her opponent Ms Sharkie may not get help from her former party leader Nick Xenophon, who she said was taking time out to look after himself.

"If Nick wants to come up and help he knows where my tiny little campaign office is," Ms Sharkie told reporters.

South Australia's Liberals are also considering a move to dump one of their two women in the Senate, with Anne Ruston and Lucy Gichui potentially being pushed down the ticket.

Senator Ruston was confident the 250 preselectors who choose the Senate voting order would make a "wise" decision.

"I'm looking forward to going out and speaking to the preselectors," Senator Ruston told reporters.

"I'm sure that Lucy will be doing exactly the same thing.

"She's a marvellous person, but she also brings a great deal of diversity to our parliament."

Prime Minister Malcolm Turnbull rejected suggestions his party was sexist, after assistant minister Jane Prentice was booted out of her own seat in favour of her former staffer Julian Simmonds.

"The Liberal party is a grassroots political organisation and the pre-selections are determined by the membership," Mr Turnbull told Melbourne radio 3AW on Tuesday.

The five by-elections have still not been officially called, with Speaker Tony Smith still consulting over dates.