The wig made the witness look like the fifth Beatle, only he also wore eyeglasses and what was either a fake beard or one he never should have grown.

“Good morning, Officer 1661,” the prosecutor began.

“Good morning,” he replied.

“For whom do you work?”

“I work for the British Security Service.”

“Is that also known as MI5?”

“MI5,” he confirmed.

The Beatle effect was enhanced by a north of England accent, which made you wonder all the more what this particular terror case was doing in Brooklyn federal court.

The target of the alleged bomb plot was a Manchester shopping mall.

The defendant had never even visited the United States before he was extradited here from Britain.

And the proceedings on Tuesday morning had begun with a kind of British mall cop testifying about foot traffic in various parts of Manchester.

He was followed by a parade of MI5 operatives in disguise and identified only by four-digit numbers, beginning with Officer 1661, who was no less a Brit for looking more like Ringo than Bond.

Officer 1661 then confirmed the code name of the investigation to which he had been assigned in mid-2009.

“Operation Pathway.”

That investigation had come to public notice in Britain six years ago, when the then-head of counterterrorism at Scotland Yard, Bob Quick, was photographed going into 10 Downing Street while carrying a secret document in full view. The document began:

“SECRET

Briefing Note: - Operation PATHWAY

General Overview: This is a security service led investigation into suspected AQ led attack planning within the UK

Planned Detention:

Manchester x 3

Leeds x 4

Birmingham x 4”

British authorities were forced to make the arrests immediately, much sooner than they had planned. Twelve men were taken into custody, but because the case had not yet been solidified, all were subsequently released.

Among them was the man MI5 believed to be the ringleader in Manchester, Abid Naseer. The British government sought to deport him back to his native Pakistan, but he successfully contested the move on the grounds that he would likely be tortured there.

That left Naseer in Britain, a continuing embarrassment as well as a threat in the estimation of MI5, particularly because he is brighter than your average jihadi.

A solution came in the form of an indictment across the pond in Brooklyn. The indictment alleged that the Manchester plot was part of a larger conspiracy that also involved attacks in New York and Copenhagen, all overseen by the same al Qaeda handler.

Naseer fought extradition to the United States, but our torture days are behind us. He lost and landed in America in 2013. He is on trial in Brooklyn federal court in a case that had been too weak to bring in Britain.

The lead prosecutor in Brooklyn alleged during her opening argument that the proof included a letter describing the larger conspiracy that was recovered by Navy SEAL Team Six when it killed Osama bin Laden.

But the core of the case was British. The moment came on Monday when a Brit in a bad wig and what was assumed to be a fake nose requested and received a closed-door conference with Judge Raymond Dearie to explain the importance of not allowing courtroom artists to draw the faces of the MI5 agents who would be testifying. The judge came out seeming duly warned.

“The situation is grave,” Dearie said.

The lone artist in the courtroom on Tuesday obeyed the judge’s order to leave the face blank as the Beatle-wigged Officer 1661 recounted his role in Operation Pathway. The officer described following Naseer, who had been given the code name “Small Panel.” The jury was shown surveillance photos that had been taken on British streets of the defendant along with pals who were identified only by their code names.

“That is Glass Pendant and Happy Skater with Small Panel,” Officer 1661 said of one photo that appeared on a wall screen as well as computer monitors in the jury box.

Officer 1661 said he had at one point trailed Naseer to a Liverpool “coach station.”

“Can you tell us the difference between a coach and a bus?” the prosecutor asked.

Officer 1661 explained that a bus generally operated within a city, whereas a coach went from one city to another. A question that went unasked and unanswered was what Naseer’s seemingly uneventful travels had to do with the case.

The prosecutor’s last question was clearly meant to cast in doubt on Naseer’s insistence during the opening arguments that when he spoke in emails about a “wedding,” he was not using an al Qaeda code word for an attack, as the government alleged. Naseer insisted he had been speaking of his intention to marry a real-life woman.

“Did your ever observe the defendant in the company of a woman?” the prosecutor now asked.

“No, I did not,” Officer 1661 replied.

As Naseer had decided to act as his own attorney, he then got an opportunity to cross-examine the witness.

“Good morning, Officer 1601,” Naseer said.

“1661,” Officer 1661 corrected him.

Naseer asked if he had ever given Officer 1661 cause for alarm or suspicion during the weeks of surveillance.

“No,” Officer 1661 replied.

The next witness was Officer 1488, who proved to be a woman in bobbed wig, glasses, and red lipstick. Naseer chose not to ask her any questions, though he did cross-examine the male agents who followed her to the stand, Officer 1498 in a wig, then Officer 8848 with what appeared to be a fake nose.

A second courtroom artist had appeared, and per the judge’s order both had to clear their drawings with the prosecutor and the MI5 supervisor in the bad wig who had conferred with the judge the day before. The MI5 supervisor was rapidly clenching his jaw and seemed oddly wound up.

He may have been fearing some security breach to follow the bumble with the secret document outside 10 Downing Street.

Or the poor man may have been aware that people in the courtroom had been examining his decidedly prominent nose and debating whether it was fake as well.

To have asked him would have seemed impossibly rude, and the question remained unresolved.

At least everybody went home knowing the difference between a coach and a bus.