A SCOTTISH MP has written to police asking them to investigate the expenses of the under-fire Culture Secretary Maria Miller.

Thomas Docherty, the Labour MP for Dunfermline and West Fife, said Scotland Yard should look seriously at the Tory MP's claims.

The move came on another difficult day for Mrs Miller and her party leader David Cameron, following allegations a newspaper was warned to remember plans for greater media regulation before writing stories about her expenses.

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Mr Cameron also faced criticism for claiming three members of the public had had a casting vote on the MP-led committee that cleared Mrs Miller of breaking strict expenses rules earlier this week.

In fact, the lay members of the Commons Standards Committee do not have a vote.

There were also renewed calls for MPs to be prevented from sitting in judgement on themselves and demands for Mrs Miller to be sacked or stripped of responsibility for shaping a new press regulator.

Mr Docherty said: "The independent Standards Commissioner raised significant and serious issues about the basis on which Maria Miller claimed more than £40,000 of taxpayers' money.

"The Metropolitan Police have a duty to investigate these issues thoroughly."

On Thursday Mrs Miller was cleared of breaking the rules by moving her parents into her taxpayer-funded second home.

However, she was ordered to pay back £5800 in mortgage expenses and to make a humiliating apology to MPs.

That 31-second statement drew heavy criticism amid claims her tone had been "contemptuous" .

She is also thought to be the first minister to make such a statement to the Commons without resigning.

The cross-party Standards Committee overruled sleaze watchdog Kathryn Hudson in ordering Mrs Miller only to pay £5800.

Ms Hudson had originally suggested that the Tory MP hand back £45,000 in over-claimed mortgage interest.

Letters published alongside the committee report show Mrs Miller repeatedly attempted to close down the long-running investigation.

And they reveal that in January this year Ms Hudson accused the culture secretary of trying to "discredit" her. Another Labour MP, John Mann, has called for the committee to publish all minutes of its deliberations.

Mr Mann, whose complaint triggered the investigation, also called for Mrs Miller to be stripped of her responsibility for shaping a new press regulatory system.

Mrs Miller sold her London property, purchased for around £235,000, for just under £1.5 million in February.

Labour frontbencher Chi Onwurah accused the Conservative leader of letting the minister, now of the few women around his cabinet table, "off the hook".

Ex-Daily Telegraph editor Tony Gallagher told the BBC that while investigating Mrs Miller's expenses her special adviser Joanna Hindley and Mr Cameron's spokesman Craig Oliver had both suggested he bear in mind the Leveson inquiry into press ethics. Downing Street insisted Mr Oliver had not threatened Mr Gallagher.