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A political scandal is swirling in Britain. But Boris Johnson is unlikely to drain the swamp

London(CNN) Much of Donald Trump's success early in his political career came from his promises to "drain the swamp" of Washington DC. The former US president was referring to the enormous power held by wealthy lobbying groups who try to influence government officials to make policy decisions that might benefit the interests of those they represent.

While DC is often referred to as the global capital of lobbying, the truth is American transparency laws and restrictions on what public officials can actually do in office limit the influence these individuals could have. Of course, it has been pointed out by numerous critics of the former president that he more than nearly any other president blurred the lines between governing and the personal interests of his associates.

A short hop over the Atlantic and the story is very different. Former British Prime Minister, David Cameron, is embroiled in a scandal in which he allegedly used his personal connection to the Chancellor of the Exchequer, Rishi Sunak, to try to secure government funds to prevent a financial services company he worked for from collapsing during the pandemic.

Cameron was the Conservative prime minister from 2010-2016. Sunak first entered parliament as a Conservative in 2015, under Cameron's leadership.

The firm, Greensill Capital, did not ultimately receive the loan from the Covid Corporate Financing Facility that Cameron was requesting, but did receive funds from a different support scheme called the Coronavirus Large Business Interruption Loan Scheme, government minister Paul Scully confirmed in Parliament on Tuesday.

Greensill, now insolvent, focused on supply chain financing, which helps companies get paid sooner for their services through short-term loans.

Needless to say, most business owners don't have the luxury of a former PM on their staff who happens to be the current Chancellor of the Exchequer's old boss, and can text him personally. And it's pretty rare for the company's chief executive and founder to be a former unpaid adviser to that former prime minister.

However, Lex Greensill was so embedded in the corridors of power here in Westminster that he even had his own Downing Street business card, which the opposition Labour party has been only too happy to leak to journalists in recent days.

The opposition Labour party has leaked the Downing Street business card of Lex Greensill.

Government officials have confirmed to CNN that Greensill was a supply chain finance adviser between 2012 and 2015, but say he didn't formally work in 10 Downing Street.

The Treasury published two texts sent by Sunak in reply to Cameron on April 3 and 23, 2020 respectively which, while non-committal, did say he had "pushed the team to explore an alternative with the Bank that might work." The Treasury declined to publish Cameron's texts.

Cameron has since published a statement confirming that he messaged Sunak about rescuing the firm, that Greensill had a job in Downing Street during his time as PM, confirming that he worked 25 days a year for the bank and, bizarrely, admitting to going on a trip to Saudi Arabia with Greensill in 2020 to meet with Crown Prince Mohammed Bin Salman to "advise on their forthcoming chairmanship of the G20." Cameron says he only met with Greensill "twice at most" during his time as PM.

Perhaps more problematically, he also admitted that he'd lobbied numerous others to discuss using Greensill services in the UK's publicly funded National Health Service. The particular service he was requesting the government use was being offered free of charge by Greensill as part of its Corporate Social Responsibility program.

Cameron defended his intervention as not motivated by his own financial gain, but in order to protect the numerous companies and jobs that Greensill financed. Cameron says he broke "no government rules," but did, admit that "communications with government need to be done through only the most formal of channels, so there can be no room for misinterpretation." CNN has requested comment from both Cameron and Greensill, but has yet to receive a reply.

David Cameron, then prime minister, stands with then London mayor Boris Johnson before the 2012 London Paralympics.

Sunak has defended his actions, saying it's right that his department "engages with stakeholders and considers policy suggestions that are put to us, especially in an unprecedented crisis."

Downing Street declined to comment further, other than to say "all the issues relating to Greensill will be considered under the review."

It's hard to find any way in which this doesn't look phenomenally grubby, from the inside or outside. That might explain why current Prime Minister Boris Johnson has failed to publicly support Cameron, and has ordered an independent inquiry into his behavior.

However, anti-corruption campaigners in the UK are skeptical that any good will come of this inquiry.

"The UK's real problem is that whilst we do have procedures in place to regulate lobbying and post-government appointments, they are just woefully inadequate," says Daniel Bruce, chief executive of Transparency International UK.

Bruce points out that the two specific mechanisms that are relevant to the Cameron scandal are particularly weak.

First, the Register of Consultant Lobbyists, the only formal list of those lobbying the UK government, only captures people lobbying for companies or bodies who are external consultants. Bruce's organization estimates that the vast majority "of lobbying is done by people who work directly for the person they are lobbying on behalf of," says Bruce.

In the case of Cameron and Greensill, Cameron was a contracted employee for the firm, so sidesteps the register policy -- which was introduced by Cameron's government in the first place.

Labour Party is already using the scandal to attack Chancellor Rishi Sunak.

Second, Bruce points to the Advisory Committee on Business Appointments, which advises whether or not people like Cameron should take postings once they have left office.

"This one is absolutely unfit for purpose. Even if it does find any wrongdoing, the worst punishment it can deliver is a strongly worded letter," says Bruce.

Any inquiry into Cameron's behavior is likely to find that he breached no rules. And if that inquiry fails to look at the broader issues surrounding lobbying -- and the toothless bodies that regulate it -- future scandals remain inevitable.

The inadequate rules on elected officials possibly cashing in on their position sadly extend to those who are currently in government, not just ex-officials who are looking to get rich post-office.

"The only real protection we have from government sleaze is an apolitical civil service telling ministers what they can and cannot do," says Jolyon Maugham, director of the Good Law Project, a non-profit organization that uses law to protect public interest.

"Yes, we have a ministerial code, we have registers of financial interest. But breaching the ministerial code doesn't mean you'll get sacked. And very few MPs have stopped filling their pockets because of public shame," Maugham adds.

The fact that the UK doesn't have a codified constitution to protect against this kind of alleged abuse is a constant source of irritation for many. Maugham points out that "America is a modern country whose founders foresaw the potential for abuses of power, but the UK has never really had anything like that."

The Cameron scandal comes at a time when there is pressure for Johnson's government to address stories that during the coronavirus pandemic, it more often awarded lucrative government contracts to people connected with the administration. So, you'd be forgiven for thinking that Sunak's involvement would be an extra source of aggravation for ministers trying to shake accusations of cronyism.

Indeed, the opposition Labour Party is already using the scandal to attack Sunak, a man who has variously enjoyed positive press for much of his response to the pandemic.

Bridget Phillipson, Labour's Shadow Chief Secretary to the Treasury, says that the Chancellor "is happy to stand in front of a camera when it suits him and splash public cash on boosting his brand, but won't answer questions about his involvement in the biggest lobbying scandal for a generation."

Boris Johnson's government is under pressure over stories that it more often awarded lucrative government contracts to people connected with the administration.

However, neither of these stories are likely to give Johnson the appetite to drain Westminster's lobbying swamp.

"The public rarely pays attention to these stories because they already assume this level of corruption is happening," says Ben Page, chief executive of polling firm Ipsos MORI. He adds that even in the case of the Covid cronyism, "the public repeatedly shows that its priority is getting through the pandemic at all costs. If at a time of crisis that means giving contracts to friends to get the job done, it's unlikely to make a significant difference to support for the government."

Government sources say that their own internal research shows similar results and that if the UK's pandemic is over sooner rather than later, these sorts of scandals will be a minor issue compared to the public relief. A minister told CNN that they are confident that even if stories emerge that people connected to the government won contracts in a public crisis, they will be forgiving of the fact these were not normal times, especially in areas that have been successful, like the vaccine rollout.

Washington DC's reputation for influential lobbyists is obviously justified. If it wasn't, Trump's anti-swamp rhetoric wouldn't have found such a keen audience. But in reality, for all the money that exists in American politics, the UK trails behind when it comes to stamping down on this type of grubbiness.