The first meeting with Boris Johnson that Jennifer Arcuri described as an “electrifying” encounter was caught on camera, the Guardian can reveal.

The picture emerged as files relating to allegations of misconduct against the prime minister over his links to the US businesswoman were due to be handed to the police watchdog.

The documents are central to allegations that Arcuri was given favourable treatment due to her friendship with Johnson when he was mayor of London.

They include emails showing that Arcuri was given a coveted place on trade missions by Johnson’s office despite failing to meet the criteria for a place.

Messages suggest that officials at the mayor’s promotion agency, London & Partners, which ran the missions, were overruled by the mayor’s team when they refused her a place on trips to New York and Tel Aviv that Johnson attended.

One of the L&P emails said: “She [Arcuri] has been speaking to Boris and [name redacted] about her being in NY and they are both, apparently, happy with that. So we should treat her as simply another member of the London tech community.”

It is understood the redacted name of the adviser is due to be released to the Independent Office for Police Conduct as it decides whether to launch an investigation into allegations of misconduct in public office against Johnson.

An official at the Greater London authority formally referred the allegations to the IOPC last month because Johnson headed the mayor’s office for policing and crime as part of his role. It is expected to make a decision on whether to investigate by the end of October.

The prime minister has insisted “full propriety” was followed and he has no interest to declare over Arcuri.

This week, Arcuri confirmed she shared a “very close bond” with Johnson, but she insisted she was not given favourable treatment by the then mayor or his officials. She also denied that £126,000 in public money she was awarded was related to her friendship with Johnson.

In an interview with ITV’s Good Morning Britain, she also recalled the first time she met Johnson at a gathering of venture capitalists in 2011. The Guardian has uncovered pictures of the event that took place exactly eight years ago on Friday. It was prosaically marked in Johnson’s official diary as a five-minute speech at the Landmark Hotel, Marylebone.

Jennifer Arcuri said Johnson ‘changed the complete energy of the room’ when he spoke to the gathering in October 2011. Photograph: Jim Varney

Arcuri’s recollection of the event is more vivid. She told ITV: “I turned around and there’s this guy that walks in the room with his hair all disheveled and his shirt’s untucked and papers that looked like something I pulled out of my pre-schooler’s backpack. And he comes across the room and he proceeds to speak. And suddenly he turns the entire room of grovelling, curmudgeoned, angry men into howling schoolgirls.”

She added: “It was just electrifying to see that kind of personality, change the complete energy of the room. So that’s when I was like, ‘who is this guy? I gotta go say hi’. And I walked right over and I said, Mr Johnson, my name is Jennifer Arcuri. I would really love it if you’d come speak at my venture capital event.”

Johnson went on to speak at four events run by Acuri’s start-up company, Innotech, and she claims visited her Shoreditch flat up to 10 times. The pair also went on three EU-funded trade missions to Kuala Lumpur, New York and Tel Aviv.

During the Kuala Lumpur trip in December 2014, Arcuri met Johnson’s half brother Max, who was then based in Hong Kong for Goldman Sachs. She was pictured by the mayor’s tech ambassador, Eileen Burbidge, with Johnson’s younger brother alongside one of the mayor’s deputies, Richard Blakeway, at the UK high commissioner’s residence in Kuala Lumpur.

at high commissioner's residence in Kuala Lumpur, l to r @davisonandy, Rick Blakeway, @maxjohnson_27 @jennifer_arcuri pic.twitter.com/OO7L2niYzT — Eileen Burbidge (@eileentso) December 1, 2014

A selfie by Arcuri at the same event showed her with Max Johnson and Gordon Innes, the then head of L&P.

A letter from the prime minister’s lawyers sent on Monday said that the London assembly’s oversight committee had no right or remit to investigate his relationship with Arcuri.

The committee asked Johnson to explain how grants and privileged access to trade trips were awarded to Arcuri during his time as mayor.

The letter, which was leaked to HuffPost, said the oversight committee “is not and should not be in effect a standards body” and that “they may be exceeding their remit or overstepping the mark by requiring this information of our client”.

The committee chair, Labour’s Len Duvall, has asked for legal advice about whether the watchdog can discuss the letter at an open meeting next Wednesday.

The meeting is also expected to decide whether the committee should use its powers to summon the former mayor to answer questions in person, as it did over his failed garden bridge project.

Allen Simpson, strategy and corporate affairs director at L&P, said: “We have received an information request from the IOPC and are complying with it in full. We will continue to do so.”