The Coalition, which had been pressing for Mr Feeney to resign, immediately ramped up calls for the resignation of Queensland Labor MP Susan Lamb, who failed to renounce her British citizenship before the 2016 election because of a problem with her paperwork.

Ms Lamb is one of a number of Labor MPs still facing questions over their eligibility.

Defence Industry Minister Christopher Pyne said it was clear Ms Lamb was still a UK citizen.

"The advice from her own barrister indicates she's never relinquished her UK citizenship. Bill Shorten now faces the prospect that he must cause Susan Lamb to resign," Mr Pyne said.

Mr Feeney said on Thursday he had been unable to find sufficient evidence of his British renunciation.

"On this basis, having regard for my duty under section 44 of the constitution, I have today written to the Speaker of the House of Representatives resigning as an MP effective immediately," he said.

The Victorian MP revealed last December he had been unable to find paperwork that proved he had renounced his British citizenship before being elected in 2007, and was referred to the High Court.

Opposition Leader Bill Shorten paid tribute to Mr Feeney for his work in the defence portfolio and thanked him for his service to the ALP, but said his decision to step down was the right one "and spares the valuable time and resources of the High Court".

Senior Labor figures in Victoria said Ms Kearney, who has already been pre-selected for the Victorian state seat of Brunswick, was Mr Shorten's first choice for Batman.

"Running her is a signal of how serious we are about winning this seat, we will put everything we can into winning this seat," one MP said.

Ms Kearney did not respond to a request for comment.

The Greens candidate in 2016, Alex Bhathal​, is expected to run again although some in the party do not want her to stand.

The Greens came desperately close to winning Batman at the 2016 election, where they gained a 9.5 per cent swing and Ms Kearney will face a tough fight to retain it for Labor.

Ms Bhathal received about 900 more first preference votes than Mr Feeney, who relied on Liberal preferences to be re-elected.

Liberal state director Nick Demiris said in November that the party might not field candidates in inner-Melbourne electorates in future.

On Thursday, a senior Liberal source confirmed it was the party's intention to sit out the Batman byelection, likely making Labor's task much tougher.

Greens Leader Richard Di Natale made it clear his party would be hammering Labor in Batman over its asylum seeker policies and the proposed Adani coal mine in Queensland.

"That huge polluting coal mine will be one of the major issues of this election campaign," Senator Di Natale said.

Many voters in Batman will return to the polls for the second time in less than six months following November's Northcote byelection.

Among them is barber Adam Volkmer, 39, who has lived in Northcote for 15 years.

He said he was a Labor voter with "one foot in the Green camp" and had seen the area become more educated and left-leaning.

"I'll probably vote Labor. As I get older I'm becoming more conservative but I think that just happens," he said.

"I guess there is that idea that a Greens vote is a waste of your vote."

Paul Green, who has owned Greens Furniture on High Street for 35 years, said he was a former Labor voter who had switched camps to the Greens.

He labelled Mr Feeney a disappointment.

"I'll definitely vote Greens," he said.

"The Greens are just what Labor was to me when I started voting 35 years ago. For me, their policies are more switched on and relevant to the world we're living in now."