Bronwyn Bishop has resigned from her role as Speaker, buckling under pressure generated from her travel expenses scandal.

Prime Minister Tony Abbott announced the move at a press conference on Sunday afternoon, also flagging a review into parliamentary entitlements just 15 months since rules were last tightened for MPs’ expenses.

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Fresh allegations of Mrs Bishop’s extravagant taxpayer-funded travel have almost become a daily occurrence since it was revealed she spent over $5000 on a chartered helicopter flight to attend a Liberal Party function.

Mr Abbott announced a fundamental “root and branch” review of MPs entitlements. “It won’t just be tinkering with the system,” he told reporters in Sydney.

“Plainly the system that we have is deficient. The public deserves to be absolutely confident taxpayers’ money is not being abused.”

The prime minister said Mrs Bishop had done the right thing by the parliament and the people of Australia.

Sunday was not the day to offer an appreciation of her long political career and contribution to public life, Mr Abbott said.

The review will be carried out by former Finance Department head David Tune and head of the Remuneration Tribunal John Conde.

Mr Abbott insisted the review would not be a “quickie” but declined to give a specific time frame.

The prime minister refused to divulge details of his conversation with Mrs Bishop, who he acknowledged as one of his friends.

“This has obviously been a very difficult day for Bronwyn Bishop,” Mr Abbott said.

In a statement, Mrs Bishop said she had tendered her resignation effective immediately.

“I have not taken this decision lightly,” she said.

“It is because of my love and respect for the institution of parliament and the Australian people that I have resigned as Speaker.”

Mrs Bishop said she looked forward to continuing to serve voters in her electorate of Mackellar.

Opposition Leader Bill Shorten kept up his attack on Mr Abbott over the affair by accusing the Prime Minister of blaming the system rather than the Speaker.

“Unfortunately Tony Abbott still won’t accept that Bronwyn Bishop has done anything wrong,” Mr Shorten said in a statement.

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

“Mrs Bishop hasn’t resigned because it was the right thing to do, it was because she and Mr Abbott realised they had no other choice.”

Earlier on Sunday, Mr Shorten accused Mr Abbott of being more afraid of Mrs Bishop than the Australian people, as he increased pressure on the Prime Minister to “show some courage” and tell the embattled Speaker to resign.

Federal MP Clive Palmer tweeted in 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”.

Congratulations #BronwynBishop for finally listening to Australian public & resigning as #Speaker #byebyebronwyn #auspoI

— Clive Palmer (@CliveFPalmer) August 2, 2015

Bronwyn Bishop was an excellent Speaker, is a great friend and remains a valued colleague.

— Christopher Pyne (@cpyne) August 2, 2015

‘Mystery’ flight and wedding engagements

Mrs Bishop was under fire for a series of allegations into travel rorts, which her office had said were taken within her entitlements.

On July 15, it was revealed that Mrs Bishop spent $5227 on a charter helicopter to travel a short distance from Melbourne to Geelong for a political fundraiser in November 2014.

Questions were then raised about a $600 expense claim by Mrs Bishop, while also attending a wedding of former Liberal colleague Sophie Mirabella in Albury, in 2006.

Then News Corp reported on Wednesday that Mrs Bishop hit the public purse again for $288 in travel allowances, to stay in Brisbane on the night of MP Teresa Gambaro’s wedding in April 2007.

The details were released by the Department of Finance in June as part of a six-month audit into the expenses racked up by serving and former federal politicians for the second part of 2014 – revealing Mrs Bishop’s total spend was $398,563.

She is ranked seventh out of the top 10 spenders for that period, and one of the biggest spenders in parliament if you leave out once-off office fit-out costs.

On Wednesday, Independent MP Andrew Wilkie said fellow MP Clive Palmer would move a motion of no confidence and he would second it, if the Speaker did not stand down before parliament resumed on August 10.

Mrs Bishop apologised to the nation and admitted to an “error of judgement” on radio station 2GB on Thursday morning. She swore to repay the cost of flights to the weddings of Liberal colleagues.

– with AAP