The case is expected to take several weeks to resolve, with legal experts predicting that the judge is unlikely to side with the foundation’s argument because immigration documents contain a wealth of personal information about the applicant and so ordering the release of Prince Harry’s would set a potentially dangerous precedent.

Stacy Cozart Martin, an immigration lawyer and professor at Case Western Reserve University, told the BBC: “Those applications have a tonne of personal information on them. It would be very, very shocking, and I think a little frightening, if that were to be released to the public. Not only for him, but as a whole.”

DHS said the think-tank had failed to demonstrate the necessity of releasing the document and questioned whether there was truly “widespread” public interest in the matter.

Prince Harry’s spokespeople have so far said they will not comment “at this time”.

The case opened in a federal court in Washington DC on Tuesday 6 June, with Judge Carl Nichols ruling that the Biden administration had one week to decide how it would handle the foundation’s FOIA request.

Representing the US government, assistant US Attorney John Bardo argued in court that sufficient coverage from mainstream American media was required for a request to be expedited.

Mr Dewey countered that DHS regulations simply say “media” without specifying where the outlets are based, pointing out that news websites have a global audience online these days, no matter where their parent company might be situated.

“You can’t define mainstream,” he subsequently told The Independent. “That’s almost absurd in this context. So as a policy matter, that is a very alarming statement for the press and for transparency for the administration.”

“We are calling for accountability, transparency and openness from the Biden presidency,” Nile Gardiner, the director of the Margaret Thatcher Center for Freedom at the foundation, said after last week’s hearing. “We believe there is a tremendous public interest in the release of these records in order to establish that US immigration law is fair, [that] it applies equally to everyone.”

“It is our view, definitely, that the public needs to see these ... documents and [what] exactly what Prince Harry put down on his application, especially in relation to his widespread drug use admitted to in Spare,” he added.

Dr Gardner said the foundation wants “to establish whether or not any favours were granted to Prince Harry, whether there was a preferential treatment given to Prince Harry in any way”.

The director of the Oversight Project at The Heritage Foundation, Mike Howell, told reporters after the hearing that “the everyday American is absolutely sick and tired of globalist elites lecturing us, looking down at us, dominating our cultural institutions, and no one proves that point more than Prince Harry”.

“They’re also sick and tired of a broken immigration system, one that we see a dual standard at play every single day,” he added.

Prince Harry wrote in Spare that cocaine “didn’t do anything for me”.

“Marijuana is different, that actually really did help me,” he added.

Three agencies within DHS, including USCIS and US Customs and Border Protection, have rejected the FOIA request, but DHS HQ has so far not responded, with Mr Bardo saying during the hearing that no search for the files has been conducted at DHS HQ.

DHS said in legal filings that the US Customs and Border Protection denied the requests because Prince Harry hasn’t consented to the release of the files, with Mr Bardo saying in court that an individual’s visa is “confidential”.

Speaking to reporters outside the DC federal courthouse, Mr Dewey said that Prince Harry had foregone his right to privacy after his series of highly publicised interviews and Netflix documentary series.

Mr Dewey argued in court that the case is part of a larger probe into the conduct of the federal government, specifically into DHS supposedly not following the law in other areas of its responsibilities, such as not protecting the US border with Mexico.

“What are we asking for here?” Mr Dewey told reporters outside the courthouse. “We are only asking for the records that are related to this question that has been raised about the drug use and admission ... he’s talked about it, he’s written about it extensively, he has waived any privacy interest he has in his drug use, he has bragged about it in Spare and sold that.”

If the duke’s application were to be published and reveal that his answers contradicted his later public revelations about his dalliances with drugs, the case would call into question the Biden administration’s handling of the visa application process, the organisation contends.

In a statement, the Heritage Foundation said that it hopes to determine whether “celebrity elites” such as the Duke of Sussex were likely to receive preferential treatment and whether the DHS was operating “fairly – without fear or favour”.

Speaking to Sky News, its counsel Sam Dewey said: “The [US] government has taken the position that ‘there’s nothing to see here’.

“We’ve taken the position that no, if you look through all the details of his admissions, you look at the drug laws, you look at the laws on admissions, there’s a real serious question as to whether or not he should have been admitted.

“The alternative, if he didn’t disclose the drug use – then there’s a very serious question as to whether or not proceedings should have begun against him for that.”

Large parts of last week’s hearing centred on the amount of media attention on Prince Harry and his supposed drug use which some legal experts say would have barred him from entering the US.

The Heritage Foundation has suggested that the federal government may have been engaging in favouritism and may have turned a blind eye to actions which may have caused the authorities to reject the visa application. The foundation also argued that the public should be allowed to see Prince Harry’s immigration records to see if he may have provided untruthful answers.

For the government, US Assistant Attorney John Bardo argued that sufficient coverage from mainstream US media was required for a request to be expedited. He mentioned outlets such as The New York Times, The Washington Post, The Wall Street Journal and the TV networks.

Heritage lawyer Samuel Dewey meanwhile argued in front of Judge Carl Nichols that DHS regulations simply say “media” without specifying where the outlets are based.

Mr Dewey told The Independent that “you can’t define mainstream. That’s almost absurd in this context. So as a policy matter, that is a very alarming statement for the press and for transparency for the administration”.

Nile Gardiner, the director of the Margaret Thatcher Center for Freedom at the foundation, added: “I do find it astonishing that the British press is referenced as obscure.”

“These are big publications with a wide global reach including millions of Americans who read these newspapers and I find it absolutely astonishing this description today [that there’s] some media that actually count and matter and others that do not. That is an extraordinary statement to make and absolutely unacceptable,” he added.

Mr Dewey argued in court that today’s media is global, noting that The Daily Mail had 100 million page views in the US in the month of April.

The think-tank insists the application is of “immense public interest” in light of the duke’s subsequent confessions of past illegal drug use as a teenager and as an adult, which he made in the Netflix series Harry & Meghan in his recent memoir Spare.

The duke wrote in Spare that he had taken cocaine but found it “wasn’t much fun, and it didn’t make me particularly happy, as it seemed to make everyone around me” and said of smoking cannabis while still a pupil at Eton, the prestigious Berkshire private school: “Marijuana is different, that actually really did help me.”

A US DS160 visa application form explicitly asks the applicant to answer truthfully to the questions, “Have you ever been a drug abuser or addict?” and, “Have you ever violated, or engaged in a conspiracy to violate, any law relating to controlled substances?”

DHS has so far not responded to the request, prompting legal action from the foundation, in which they pointed to Prince Harry’s previous admissions of drug use, such as in his memoir Spare.

The department argued that an injunction to force DHS to expedite the request shouldn’t go ahead as the foundation hasn’t shown how they will suffer irreparable harm if the information isn’t shared.

Representing the government, Assistant US Attorney John Bardo argued on Tuesday that it wouldn’t make a difference when the request was handled, even if the response came a year from now.

The Heritage Foundation said the interest in Prince Harry’s immigration status would decrease over time.

Prince Harry has been giving evidence at the High Court in London this month as part of a landmark legal action against Mirror Group Newspapers, which he is suing for damages after alleging that journalists at its titles had resorted to underhand methods to secure stories about him and his family, including phone hacking, gaining information by deception and employing private investigators for unlawful activities.

“How much more blood will stain their typing fingers before someone can put a stop to this madness?” he wrote in his 55-page witness statement, accusing the tabloid media of bad practice.

But the Duke of Sussex, 38, is also currently the subject of a second court case underway on the other side of the Atlantic.

A request for the form under the Freedom of Information Act (FOIA) was previously turned down by US Customs and Border Protection, which told the foundation that it would need Prince Harry’s consent in order to do so.