Mike Schroepfer, Facebook’s chief technology officer, was the second executive Facebook offered up to answer questions from parliament’s select committee for Digital, Culture, Media and Sport (DCMS).

He took his place in the hot seat in the wake of the first attendee, Simon Milner, Facebook’s (now ex-) head of policy for Europe, who answered a series of questions about Cambridge Analytica’s non-use of Facebook data that came back to haunt the company in the furore that followed the Observer and New York Times revelations from Christopher Wylie.

Schroepfer is Facebook’s nerd-in-chief. He was the tech guy sent to answer a series of questions from MPs about how his platform had facilitated what appeared to be a wholesale assault on Britain’s democracy, and though there was much he couldn’t answer, when he was asked about spending by Russian entities directed at British voters before the referendum, he spoke confidently: “We did look several times at the connections between the IRA [the Kremlin-linked Internet Research Agency] … and the EU referendum and we found $1 of spend. We found almost nothing.”

But new evidence released by the United States Congress suggests adverts were targeted at UK Facebook users, and paid for in roubles, in the months preceding the short 10-week period “regulated” by the Electoral Commission but when the long campaigns were already under way.

This is the latest episode in a series of miscommunications between the company and British legislators, which has come to a head in the week the Electoral Commission finally published the findings of its investigation into the Leave.EU campaign.

Damian Collins, the chair of the DCMS committee, said: “We asked them to look for evidence of Russian influence and they came back and told us something we now know appears misleading. And we’re still waiting for answers to 40 questions that Mike Schroepfer was unable to answer, including if they have any record of any dark ads.

“It could be that these adverts are just the tip of the iceberg. It’s just so hard getting any sort of information out of them, and then not knowing if that information is complete.”

Leave.EU supporters celebrate the Leave vote in Sunderland after polling stations closed in the Brexit referendum. Photograph: Toby Melville/Reuters

Preliminary research undertaken by Twitter user Brexitshambles suggests anti-immigrant adverts were targeted at Facebook users in the UK and the US.

One – headlined “You’re not the only one to despise immigration”, which cost 4,884 roubles (£58) and received 4,055 views – was placed in January 2016. Another, which accused immigrants of stealing jobs, cost 5,514 roubles and received 14,396 impressions. Organic reach can mean such adverts are seen by a wider audience.

Facebook says that it only looked for adverts shown during the officially regulated campaign period. A spokesperson said: “The release of the set of IRA adverts confirms the position we shared with the Electoral Commission and DCMS committee. We did not find evidence of any significant, coordinated activity by the IRA operatives directed towards the Brexit referendum.

“This is supported by the release of this data set which shows a significant amount of activity by the IRA with only a handful of their ads listing the UK as a possible audience.”

Collins said that the committee was becoming increasingly frustrated by Facebook’s reluctance to answer questions and by founder Mark Zuckerberg’s ongoing refusal to come to the UK to testify.

Milner told the committee in February that Cambridge Analytica had no Facebook data and could not have got data from Facebook.

The news reinforces MPs’ frustrations with a system that last week many of them were describing as “broken”. On Friday, 15 months after the first Observer article that triggered the Electoral Commission’s investigation into Leave.EU was published, it found the campaign – funded by Arron Banks and endorsed by Nigel Farage – guilty of multiple breaches of electoral law and referred the “responsible person” – its chief executive, Liz Bilney – to the police.

Banks described the commission’s report as a “politically motivated attack on Brexit”.

Leading academics and MPs called the delay in referring the matter to the police “catastrophic”, with others saying British democracy had failed. Liam Byrne, Labour’s shadow digital minister, described the current situation as “akin to the situation with rotten boroughs” in the 19th century. “It’s at that level. What we’re seeing is a wholesale failure of the entire system. We have 20th-century bodies fighting a 21st-century challenge to our democracy. It’s totally lamentable.”

The big picture here is it’s possible for an individual or group with lots of money to change the course of history Damian Tambini, LSE

Stephen Kinnock, Labour MP for Aberavon, said it was unacceptable that the Electoral Commission had still not referred the evidence about Vote Leave from Christopher Wylie and Shahmir Sanni – published in the Observer and submitted to the Electoral Commission – to the police. He said: “What they seem to have done, and are continuing to do, is to kick this into the long grass. There seems to be political pressure to kick this down the road until Britain has exited the EU.”

He accused the commission of ignoring what he considered key evidence, including about Cambridge Analytica. The commission had found Leave.EU guilty of not declaring work done by its referendum strategist, Goddard Gunster, but said it had found no evidence of work done by Cambridge Analytica.

“The whole thing stinks,” Kinnock said. “I wrote to the commission with evidence that the value of work carried out by Cambridge Analytica was around £800,000. The glib way it dismissed the multiple pieces of evidence about the company was extraordinary. I just think it is absolutely not fit for purpose.”

Gavin Millar QC, a leading expert in electoral law at Matrix Chambers, said: “Our entire democratic system is vulnerable and wide open to attack. If we allow this kind of money into campaigning on national basis – and the referendum was the paradigm for this – you have to have an organisation with teeth to police it.”

Damian Tambini, director of research in the department of media and communications at the London School of Economics, described the whole system as broken and said there was not a single investigatory body that seemed capable of uncovering the truth. “The DCMS Select Committee has found itself in this extraordinary position of, in effect, leading this investigation because it at least has the power to compel witnesses and evidence – something the Electoral Commission can’t do. It’s the classic British solution of muddling through.

“The big picture here is it’s possible for an individual or group with lots of money and some expertise to change the course of history and buy an election outcome. And with our regulatory system, we’ll never know if it’s happened.”

• This article was amended on 13 May 2018 to clarify that a remark from Damian Tambini referred to the DCMS Select Committee.