The Federal Opposition says it has serious concerns about the conduct of an investigation into Speaker Brownyn Bishop’s use of travel entitlements.

Labor asked the Australian Federal Police to investigate whether Mrs Bishop misused her entitlements when she chartered a helicopter to attend a Liberal Party function last year.

But police referred the case to the Department of Finance.

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The Saturday Paper has reported the Secretary of the Department, Jane Halton, told a women’s business function the issue was “an example of sexist double standards”, and that a man would not have attracted the same outrage.

Labor’s Pat Conroy said if Ms Halton made the comments, it would suggest she had pre-judged the matter, and the Department should hand over the investigation.

“I’m very concerned because it implies the secretary has already made a judgement about this case,” Mr Conroy said.

“Secondly, it reinforces the need for the Federal Police to conduct an investigation, as I’ve urged them to do.”

A spokesman for Finance Minister Mathias Cormann said it was still appropriate for the Department to conduct the investigation, and confirmed Ms Halton would still be involved.

The concern over Ms Halton’s comments comes in the wake of a call by Liberal MP Craig Laundy for a review into parliamentary travel entitlements.

Western Sydney backbencher Craig Laundy said the ongoing attention on Mrs Bishop’s use of travel entitlements has led to criticism of all MPs.

“The last 10 days I’ve been hit with it everywhere I go and I was frustrated,” he said.

“The public have questions of us, they’re questioning me on a daily basis.”

Mr Laundy — a first-term MP — said he flies economy class and uses taxis when it is not efficient to use the parliamentary ComCar service.

He echoed calls from the Greens and Senate crossbenchers for a crackdown on travel spending.

“To restore the public’s faith in us, we should be looking at how entitlements are used and enforced and monitored,” he said.

“I don’t think that’s just a matter for public confidence, I think we should be doing that all the time anyway.”