The Metropolitan Police has confirmed it has received a letter from the SNP asking it to investigate cash for honours allegations against the Conservatives.

A spokesman for the force said it is currently “considering the contents of the correspondence” but an investigation or formal assessment into the allegations has not started.

SNP MP Pete Wishart revealed on Monday he had written to the Met after a report in The Sunday Times said 15 of the last 16 Conservative Party treasurers have been offered a seat in the House of Lords after donating more than £3m to the party.

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An ex-party chairman was quoted by the newspaper as saying: “The truth is the entire political establishment knows this happens and they do nothing about it… the most telling line is, once you pay your £3m, you get your peerage.”

The Conservatives have denied there is any link between the donations and nominations to sit in the upper chamber.

A Conservative spokesman told the newspaper: “We do not believe that successful business people and philanthropists who contribute to political causes and parties should be disqualified from sitting in the legislature.”

Mr Wishart said he was “not accusing anyone of anything”, but told Sky News the claims had to be looked into.

“There’s a very clear piece of legislation dating back to 1925, which says and states that it is an offence to be awarded an honour for the giving of money,” he said.

“What we’re going to do is ask the Metropolitan Police just to see if there’s any link between all these Conservative donors giving millions and millions of pounds to the Conservative Party and finding a way into the House of Lords, which is clearly against the law.”

His call was backed by Labour’s shadow communities secretary Steve Reed, who told Sky News’ Kay Burley: “I think it is right to ask the police to look into this because it is a fact now that the background that is most likely to get you a seat in the House of Lords is being the treasurer of the Conservative Party.

“And it looks like if you donate £3m to the Tory party and become their treasurer, you get into the House of Lords. That is not acceptable. You shouldn’t be able to buy a seat in the House of Lords.”

But deputy prime minister Mr Raab defended the government, saying: “There is absolutely no question that we haven’t followed all of the rules in relation to that and nobody is suggesting that we have done anything wrong.”

He added it is his view that the SNP are “just trying to rake muck”.

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The cash for honours claims came as the spotlight was turned on MPs’ conduct following crticism over the government’s handling of the Owen Paterson lobbying scandal.

Mr Paterson, a veteran Conservative, was facing a 30-day Commons suspension after parliament’s independent sleaze investigator found he broke lobbying rules during his £110,000-a-year private sector work.

The government was forced into a U-turn after it ordered MPs to back reforming the standards system by creating a Tory-led committee and re-examining the case against Mr Paterson.

Mr Paterson then quit as an MP as he said the scrutiny was unfair for his family.