Former MI6 officer Christopher Steele’s dossier on Donald Trump was denounced by the US president and his supporters as fake. The ongoing investigation into the Donald Trump’s Russian connections, however, has shown much of it to be true. But two notable allegations have remained unproven.

Mr Trump’s personal lawyer, Michael Cohen, had vehemently denied the claim, made in the report, that he had met with Russians with ties to Vladimir Putin in Prague; insisting he had never even been to the Czech Republic. And then there was the lurid account of the US president using prostitutes while on a visit to Moscow, something which gained huge publicity and he has strongly denied.

Mr Cohen had sued Fusion GPS, an investigative firm which had commissioned Mr Steele’s report, and a news website declaring in a tweet: “Enough is enough of the #fake #RussianDossier. Just filed a defamation action against @BuzzFeedNews for publishing the lie filled document on @POTUS @realDonaldTrump and me!"

But Mr Cohen has now voluntarily dropped his legal action. It followed reports that Special Counsel Robert Mueller’s investigation into whether Mr Trump was the Muscovite Candidate in the Presidential election has found evidence that Mr Cohen had, indeed, made a trip to Prague.

The claim that Mr Trump had hired prostitutes to urinate on the bed once used by Barack and Michelle Obama, who Mr Trump hated, and the alleged filming of it by the Russians, has resurfaced in the memoirs of James Comey.

The former FBI Director, who claims Mr Trump fired him after he refused to drop the Russia inquiry, recounted the US president repeatedly bringing up, unprompted, the sex allegation, saying at one stage “there’s no way I would let people pee on each other around me. I’m a germaphobe!” The theme continued, according to memos just released by Mr Comey.

“The president said the ‘hookers’ thing’ is nonsense but that Putin had told him ‘we have the most beautiful hookers in the world’” one of them stated.

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The memos, in which Mr Trump was also shown to be speaking in unflattering terms about General Michael Flynn, his former national security adviser who has been subsequently charged by Mr Mueller, were provided to Congress at the demand of House Republicans who, it is believed, thought they would undermine Mr Comey as well as the wider Trump investigation.

The consensus is that the move has turned out to be massively counter-productive. “Honestly, I am aghast that they thought this was going to be helpful to the president and undermine Comey, therefore the FBI, therefore special counsel Mueller” commented Jack Quinn, who had acted as Bill Clinton’s lawyer. “I can’t get over the fact that they made this calculation. I am sure the president is not going to be sitting up tonight writing thank you letters to them.”

In the view of Robert Emerson, a British security analyst: “It is the simple rule that barristers follow when questioning witnesses, ‘don’t ask something without roughly knowing what the answer is going to be’. What came out was hardly flattering for Trump. There’s another reference to Russian prostitutes and Trump simply can’t seem to get away from other sex allegations.”

The claim that Mr Mueller’s team have information about Mr Cohen’s visit to Prague came following a raid on his office and home in New York by FBI agents. They were seeking information about payments made by Mr Cohen to Stormy Daniels, a porn actress, who claims that she has had sex with Mr Trump. But, according to multiple sources, there was also search for material pertaining to an investigation into alleged fraud, tax evasion, money laundering and Mr Cohen’s actions while working for Mr Trump and real estate purchases by Russian buyers.

Mr Trump denies having sex with Daniels, whose real name is Stephanie Clifford. Mr Cohen denies any wrongdoing.

While the Mueller investigation continues to expand, with Mr Trump’s former national security advisor Gen Flynn, his former campaign manager Paul Manafort, and campaign staffers Rick Gates and George Papadopoulos already charged by the Special Envoy, the President is facing difficulties finding lawyers to represent him.

Mr Cohen is now enmeshed in a serious criminal investigation and a senior member of Mr Trump’s team, John Dowd left recently after disagreement over strategy. According to reports five large, prestigious law firms have declined to defend the President in the Russia investigation.

Mr Trump has now turned to an old ally, Rudy Giuliani. His main role, the former New York Mayor told CNN, would be to interact with Mr Mueller and bring things to a conclusion, as it “needs a little push.”.

His appointment has been greeted with general derision on social media - portrayed as a sign of Mr Trump’s desperation. Mr Giuliani pointed out that he had known Mr Mueller a for a long time, since when he was mayor and the Special Counsel was the FBI Director.

There is, however, a Christopher Steele connection to Mr Giuliani and the Trump affair. During his investigation in the run-up to the US election, the former MI6 officer had been regularly supplying information to the FBI. But he became frustrated at what he saw as lack of progress in the Trump inquiry. The Bureau seemed, instead, to be devoting their resources in the pursuit of Hillary Clinton’s email transgressions.

The New York office, in particular, appeared to be on a crusade against Ms Clinton. Some of its agents had a long working relationship with Rudy Giuliani – by then a member of the Trump campaign – since his days as public prosecutor and then Mayor.

As the election approached, FBI director James Comey made public his bombshell letter saying that Ms Clinton would face another email investigation. Two days before that, Mr Giuliani talked about “a surprise or two you’re going to hear about in the next few days. We’ve got a couple of things up our sleeve that should turn things around".

After the letter was published, Mr Giuliani claimed he had heard from current and former agents that “there’s a kind of revolution going on inside the FBI” over the original decision not to charge Ms Clinton and that Mr Comey had been forced by some of his agents to announce the reinvestigation.

Democrats wanted to know at the time into how Mr Giuliani acquired this knowledge – without getting an answer. Now, with the Special Counsel’s investigation going at full steam, Mr Giuliani may find his old acquaintance Mr Mueller and his team asking him that same question, with the power to demand answers, and opening another chapter in the Trump affair.