Bronwyn Bishop has resigned as Speaker of the House of Representatives following sustained pressure over her travel expenses.

Mrs Bishop had faced fierce criticism for more than three weeks, since it was first revealed she had spent more than $5,000 chartering a helicopter from Melbourne to Geelong in November to attend a Liberal Party fundraiser.

Prime Minister Tony Abbott told reporters in Sydney on Sunday that the Government would hold a "root and branch review" of the entitlements system in the wake of the scandal.

Mrs Bishop has paid back the money for the chopper ride — plus a 25 per cent penalty — and last week apologised for the "ridiculous" expense claim.

"I have today [Sunday] written to the Governor-General and tendered my resignation as Speaker of the House of Representatives effective immediately," Mrs Bishop said in a statement.

"I have not taken this decision lightly, however it is because of my love and respect for the institution of Parliament and the Australian people that I have resigned as Speaker."

On Saturday Mrs Bishop declined to comment on reports she claimed $6,000 last year chartering a plane to fly her 160 kilometres from Sydney to Nowra.

The Finance Department is currently investigating Mrs Bishop's use of charter flights and other entitlement claims over the past decade.

Mr Abbott said the review will be conducted by former secretary of the Department of Finance, David Tune, and Remuneration Tribunal chairman John Conde and is designed to create a system that is "simple, effective and clear".

"What has become apparent, particularly over the last few days, is that the problem is not any particular individual; the problem is the entitlement system more generally," he said.

"We have a situation where spending is arguably inside the rules, but plainly outside of community expectations, and that's what needs to be dealt with once and for all."

Mr Abbott said it had been a "very difficult day" for Mrs Bishop, but she had done the right thing by the people of Australia.

"Today is not the day to offer an appreciation of Bronwyn Bishop's long parliamentary career, her long career in public life," he said.

"I have a great deal of personal respect for Bronwyn Bishop and without wanting to underplay the significance of some of the errors of judgement, which she herself has conceded and apologised for, I think she has certainly done the right thing today.

"No-one who saw Bronwyn on television the other day could be under any doubt as to her remorse."

Shorten, Wilkie say Bishop's resignation 'overdue'

Opposition Leader Bill Shorten said Mrs Bishop's resignation was "overdue and unrepentant" and called on Mr Abbott to release the findings of the Finance Department's investigation into Mrs Bishop.

"Unfortunately Tony Abbott still won't accept that Bronwyn Bishop has done anything wrong," he said.

"Mr Abbott has blamed the system, but it was Mrs Bishop's addiction to privilege that was the real culprit."

Earlier on Sunday the Labor leader declared "enough is enough" and said Mr Abbott should lean on Mrs Bishop to resign.

Independent MP Andrew Wilkie also said Mrs Bishop's resignation was overdue and urged the Australian Federal Police to investigate her use of entitlements.

"Watching this saga unfold was worse than getting your wisdom teeth out," he said.

"The Prime Minister is wrong to suggest that this comes down to the gap between current entitlements and community expectations.

"The fact is that the current entitlements rules do not allow a member or senator to go somewhere principally for private reasons and then to certify it as an official trip. To do so is fraud."

Independent senator Nick Xenophon said Mrs Bishop's resignation was an opportunity for reform of parliamentary entitlements.

"The risk here is that the Opposition will crow about Bronwyn Bishop resigning, when the big picture is that the whole system of parliamentary entitlements must be fundamentally reformed," Senator Xenophon said in a statement.

"This is not about Bishop — it's about taxpayers being treated as pawns by both sides."

Federal MP Clive Palmer tweeted on Sunday congratulating the outgoing speaker for "finally listening to [the] Australian public [and] resigning".

Mr Palmer had previously called for Mrs Bishop's resignation because of her age and because she was "very biased".

'Father of the House' Philip Ruddock touted as likely replacement

Mrs Bishop cannot be replaced until Parliament resumes next Monday, as the appointment of Speaker is through a vote of the Lower House.

It is most likely the replacement of Speaker will be the first order of business when Parliament resumes.

Coalition MPs the ABC has spoken to believe veteran Liberal Philip Ruddock is the most likely replacement for Mrs Bishop.

Neither Mr Ruddock or Nationals MP and deputy speaker Bruce Scott have said publicly whether they want the job but it is understood both could well be candidates.

However it is felt the Liberals would not want to give such a prized job to a Nationals MP, unless a deal was cut involving the Nationals giving up a ministerial role.

One Nationals MP said there was no way the party would give up a frontbench role, therefore likely ruling Mr Scott out of contention.

Mr Scott has announced he will not contest the seat of Maranoa at the next election.

Victorian Liberal Russell Broadbent is another name mentioned as a possible replacement for Mrs Bishop.

A moderate on social issues, Mr Broadbent is viewed as having a good relationship with Labor and is a member of the speaker's panel, meaning he can act in the role of deputy speaker.

Another Victorian Liberal, Sharman Stone, was also suggested as a potential candidate but none of the MPs canvassed by the ABC expected she would get the job, citing her public clashes with the Prime Minister over his leadership.

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