The information commissioner is considering taking legal action against a Canadian marketing firm with alleged links to Cambridge Analytica, after the firm refused to cooperate with her inquiry into the use of personal data during the Brexit referendum.

The commissioner, Elizabeth Denham, also suggested that two executives at the firm, AggregateIQ, misledCanadian MPs on Tuesday when they claimed to have answered all of her questions fully.

Her intervention was dramatically revealed during a session of a Canadian parliamentary committee on access to information, privacy and ethics with AIQ’s chief operating officer, Jeff Silvester, and his deputy, Zach Massingham.

The hearing was ambushed by an email to members of the committee by the British MP Damian Collins, who is chairing a related inquiry into fake news and was watching a live-stream of the Canadian inquiry.

Early in the two-hour hearing Silvester denied refusing to cooperate with Denham’s inquiry. He said: “On 17 May [2017], the Information Commission from the UK sent us a letter. We responded on 24 May. And then we didn’t hear from [Denham] again until 30 January 2018, when she sent us a letter and we replied. We have been cooperating the whole time.”

After he said this, Collins emailed members of the committee citing communication with Denham to dispute Silvester’s evidence.

During the hearing, the Canadian MP Nate Erskine-Smith said: “After my first round of questions I received a note from the chair of the UK digital and culture committee, Damian Collins. He has spoken after my questions to the UK information commissioner and she has indicated that AIQ has refused to answer her specific questions relating to data usage during the referendum campaign, and that the UK information commissioner is considering taking further legal measures to secure the information that she needs.”

Another committee member, Frank Baylis, asked Silvester: “Who’s telling us the truth, you or her?”

He replied: “If she has additional questions, I’m hopeful that she will follow up with us.” Later he added: “I’ve been 100% honest in all of my answers. We provided answers to all of the questions that she provided and offered to provide any clarification in our letter to her.”

But Denham told the Guardian: “The Canadian company AIQ has so far not answered the substance of our questions in the ICO’s investigation. Contrary to the statements made to the Canadian parliamentary committee about cooperation, in recent correspondence we were advised that the company would not answer any more questions from my office, stated it was not subject to our jurisdiction, and considered the matter closed. We are considering the legal steps available to obtain the information.”

Silvester and Massingham were also repeatedly asked about a £625,000 payment AIQ received from Vote Leave for advertising commissioned by BeLeave, amid allegations that it broke election spending rules.

Both denied that the ad campaign was being coordinated, but admitted that AIQ had access to a Google drive run by Vote Leave which contained BeLeave documents.

Massingham said the firm was aware that if the money was spent by Vote Leave on behalf of Vote Leave, this would have broken a spending cap.

Erskine-Smith asked: “Did you not think it was strange you received £625,000 from Vote Leave to spend on behalf of BeLeave ... in the context that if they spent on behalf of Vote Leave they would have gone over the limit? Did this not raise any flags for you?” He replied: “No.”

Silvester added: “When they asked us to do the work, we sent an invoice to BeLeave and then they let us know that was going to be paid by Vote Leave. That was all within a couple of days.”

Erksine-Smith said: “How is that not a coordinated campaign between Vote Leave and BeLeave?” Massingham said: “I’m not sure.”

At the end of the two-hour hearing, the chairman, Bob Zimmer, said: “We are all concerned. Something doesn’t smell right here. And I would challenge AIQ to do the right thing.”

Silvester has previously said: “AIQ has never been, and is not a part of, Cambridge Analytica or [its parent firm] SCL. AIQ has never entered into a contract with Cambridge Analytica.”