The UK’s data watchdog is seeking a warrant to search computers and servers used by Cambridge Analytica amid an investigation into the firm’s involvement in worldwide elections.
Information Commissioner Elizabeth Denham criticised CA for being "unco-operative" with her probe as she confirmed the application for a warrant to help her examine the firm's activities.
Meanwhile, further claims about CA included allegations the company offered to entrap politicians and used ex-spies to dig for dirt on potential targets.
But the firm's boss Alexander Nix claimed it was the target of media attacks because of its role in Donald Trump's successful US election campaign.
An undercover investigation by Channel 4 recorded Mr Nix suggesting ways he could help a potential client.
A reporter posing as a fixer for a wealthy client hoping to get candidates elected in Sri Lanka met with Mr Nix and other senior figures from CA.
Asked about what "deep digging" could be done, Mr Nix told the reporter: "Oh, we do a lot more than that.
"I mean deep digging is interesting but you know equally effective can be just to go and speak to the incumbents and to offer them a deal that's too good to be true, and make sure that that's video recorded, you know, these sorts of tactics are very effective instantly having video evidence of corruption, putting it on the internet, these sorts of things."
Mr Nix said they could "send some girls around to the candidate's house", adding that Ukrainian girls "are very beautiful, I find that works very well", Channel 4 reported.
Mr Nix told BBC's Newsnight the Channel 4 sting was "intended to embarrass us".
"We see this as a co-ordinated attack by the media that's been going on for very, very many months in order to damage the company that had some involvement with the election of Donald Trump," he said.
Mr Nix said he had a "huge amount of regrets about the fact that we, maybe, undertook this meeting and spoke with a certain amount of hyperbole about some of the things that we do".
He added: "I have some regrets about the way that I have represented what the company does. I certainly feel that the air of mystery and negativity that surrounds the work of Cambridge is misfounded and, as the CEO, I take responsibility for that."
CA was suspended from Facebook last week after it emerged that data on millions of users had not been destroyed as agreed.
Whistleblower Chris Wylie, a former research director at the UK-based company, told Channel 4 News a so-called data grab had been carried out on more than 50 million profiles in 2014.
Damian Collins, chairman of the House of Commons Digital, Culture, Media and Sport Committee, has called on Facebook founder Mark Zuckerberg to appear before MPs to explain his company's actions and Downing Street has also said it has concerns.
Asked about the reports, Mrs May's spokesman said: "It is absolutely right that the Information Commissioner is investigating this matter.
"We expect Facebook, Cambridge Analytica and all the organisations involved to co-operate fully."
The ICO is investigating the use of personal data for political campaign, including the activities of CA.
An investigation by Facebook at CA's London office was halted in order to allow the ICO to pursue its inquiry.
An ICO spokesman said: "On March 7, the Information Commissioner, Elizabeth Denham issued a Demand for Access to records and data in the hands of Cambridge Analytica.
"Cambridge Analytica has not responded to the Commissioner by the deadline provided; therefore, the Information Commissioner is seeking a warrant to obtain information and access to systems and evidence related to her investigation.
"On March 19, Facebook announced that it will stand down its search of Cambridge Analytica premises at the Information Commissioner's request. Such a search would potentially compromise a regulatory investigation. "