Information Commissioner Elizabeth Denham is pursuing evidence as part of her look at the company’s use of data analytics for political purposes.
She will apply to a court for a warrant on Tuesday, after Cambridge Analytica failed to respond to a deadline for access to its records.
The Prime Minister has called on the firm to “co-operate fully” with the Information Commissioner, with Downing Street describing allegations Cambridge Analytica harvested more than 50 million Facebook profiles in a data breach as “very concerning”.
The claims have prompted calls for either Facebook founder Mark Zuckerberg or another senior executive to give evidence to MPs.
The social media giant has also called off its own search of Cambridge Analytica premises at the Information Commissioner’s request, amid fears it could potentially compromise a regulatory investigation.
Conservative MP Damian Collins, chair of a House of Commons’ committee which has previously quizzed Cambridge Analytica bosses, said: “These investigations need to be undertaken by the proper authorities.”
The company, which operates in the UK and is registered in America, describes itself as one that “uses data to change audience behaviour” and worked with Donald Trump’s successful US presidential election campaign.
The latest development came as the firm denied engaging in “entrapment, bribes or so-called ‘honeytraps'” in the course of its work.
In an undercover investigation, Channel 4 News secretly filmed Cambridge Analytica’s chief executive Alexander Nix speaking to a reporter posing as a potential client from Sri Lanka.
Raising the possibility of “somebody posing as a wealthy developer” in an explanation of the company’s election services, Mr Nix said: “They will offer a large amount of money to the candidate, to finance his campaign in exchange for land.
“For instance we’ll have the whole thing recorded on cameras, we’ll blank out the face of our guy and then post it on the internet.”
Mr Nix also spoke of sending “very beautiful” Ukrainian girls to a candidate’s house, while he also added: “It sounds a dreadful thing to say but these are things that don’t necessarily need to be true as long as they’re believed.”
However, Cambridge Analytica claimed the Channel 4 News report was “edited and scripted to grossly misrepresent the nature of those conversations and how the company conducts its business”.
The company said: “Assessing the legality and reputational risks associated with new projects is critical for us, and we routinely undertake conversations with prospective clients to try to tease out any unethical or illegal intentions.
“The two Cambridge Analytica executives at the meeting humoured these questions and actively encouraged the prospective client to disclose his intentions.
“They left with grave concerns and did not meet with him again.”
Accompanying the statement on Cambridge Analytica’s website, Mr Nix added: “In playing along with this line of conversation, and partly to spare our ‘client’ from embarrassment, we entertained a series of ludicrous hypothetical scenarios.
“I am aware how this looks, but it is simply not the case. I must emphatically state that Cambridge Analytica does not condone or engage in entrapment, bribes or so-called ‘honeytraps’, and nor does it use untrue material for any purpose.
“I deeply regret my role in the meeting and I have already apologised to staff. I should have recognised where the prospective client was taking our conversations and ended the relationship sooner.”
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Facebook’s shares dropped sharply on Monday amid the claims it was used to mine the personal data of millions of users.
The allegations will also be investigated by the European Parliament, it was announced.