A director of the controversial data company Cambridge Analytica, who appeared with Arron Banks at the launch of the Leave.EU campaign, has been subpoenaed by the US investigation into possible collusion between the Trump campaign and the Russian government.

A spokesman for Brittany Kaiser, former business development director for Cambridge Analytica – which collapsed after the Observer revealed details of its misuse of Facebook data – confirmed that she had been subpoenaed by special counsel Robert Mueller, and was cooperating fully with his investigation.

He added that she was assisting other US congressional and legal investigations into the company’s activities and had voluntarily turned over documents and data.

Kaiser, who gave evidence to the UK parliament last April in which she claimed Cambridge Analytica had carried out in-depth work for Leave.EU, is the second individual connected to the firm subpoenaed by the special counsel. The Electoral Commission has said its investigation into Leave.EU found no evidence that the campaign “received donations or paid for services from Cambridge Analytica …beyond initial scoping work”.

Damian Collins, chairman of parliament’s inquiry into fake news, said it was “no surprise” that Kaiser was under scrutiny by Mueller because “her work connected her to WikiLeaks, Cambridge Analytica and [its parent company] SCL, the Trump campaign, Leave.EU and Arron Banks”.

He said it was now vital Britain had its own inquiry into foreign interference: “We should not be leaving this to the Americans.”

Tom Watson, the deputy leader of the Labour party, echoed Collins’s statement, saying: “This is the first evidence that a significant player in the Leave.EU campaign is of interested to the global Mueller inquiry. People will be bewildered that the British government has no interest in establishing the facts of what happened.”

Special counsel Robert Mueller. Photograph: Joshua Roberts/Reuters

In August, Sam Patten, a US political consultant who had worked for Cambridge Analytica on campaigns in the US and abroad, struck a plea deal with Mueller after admitting he had failed to register as a foreign agent for a Ukrainian oligarch.

He became a subject of the special counsel’s inquiry because of work done with Paul Manafort, Trump’s campaign manager, in Ukraine. He had also set up a business with Konstantin Kilimnik, a key figure who Mueller has alleged has ties to Russian intelligence and who is facing charges of obstruction of justice. In a 2017 statement to the Washington Post, Kilimnik denied any connection to intelligence services. Kaiser, however, is the first person connected directly to both the Brexit and Trump campaigns known to have been questioned by Mueller.

The news came to light in a new Netflix documentary, The Great Hack, which premiered at the Sundance film festival last month and is expected to be released later this spring. Film-makers followed Kaiser for months after she approached the Guardian, including moments after she received the subpoena. She claims the summons came after the Guardian revealed she had visited WikiLeaks founder Julian Assange while still a Cambridge Analytica employee in February 2017, three months after the US election.

One part of Mueller’s investigation focuses on whether the Trump campaign sought to influence the timing of the release of emails by WikiLeaks before the election. Investigators are looking at communications between them. In the film, Kaiser says that she has gone from being a cooperating witness to a subject of investigation because of her contact with Assange.

In October 2017, it was revealed that Alexander Nix, the chief executive of Cambridge Analytica, had contacted Assange in August 2016 to try to obtain emails from Hillary Clinton’s presidential campaign – which indictments from Mueller’s team say were obtained by Russian military intelligence – to use in Donald Trump’s campaign. When Kaiser gave evidence to parliament last year, she was asked about her relationship with Assange and WikiLeaks but failed to reveal that she had met Assange.

In the documentary, Kaiser is shown after receiving an email from the Guardian last June asking about meeting Assange and alleged donations of cryptocurrency to WikiLeaks. Kaiser did not respond to the email at the time, but on camera says: “She knows I met Assange. And she knows I donated money to WikiLeaks in bitcoin.”

Her legal representatives later wrote to the paper to say that the allegations, including that she had “channelled” donations to WikiLeaks, were false. Kaiser said she had received a small gift of bitcoin in 2011 – long before she worked at Cambridge Analytica – and, not knowing what else to do with it, gave it to WikiLeaks, because she had benefited from material it had released over the years.

Her lawyer told the Observer that the meeting with Assange came about after a chance encounter in London with an acquaintance who knew him. It lasted 20 minutes and consisted mainly of Assange telling her “about how he saw the world”. He said they did not discuss the US election.

Patten and Kaiser were involved in a controversial election campaign in Nigeria in January 2015, which former Cambridge Analytica employees say had “unsettling” parallels to the US presidential election.

The Guardian revealed that the data firm had worked alongside a team of unidentified Israeli intelligence operatives on the campaign. Ex-Cambridge Analytica employees described how the Israelis hacked the now-president of Nigeria’s emails and released damaging information about him to the press weeks before the election.