A spokesperson for Information Commissioner's Office (ICO) said investigators will "examine closely" the details of the closure and will "closely monitor any successor companies".
She said: "The ICO has been investigating the SCL Group and Cambridge Analytica as part of a wider investigation into the use of personal data and analytics by political campaigns, social media companies and others.
"The ICO will continue its civil and criminal investigations and will seek to pursue individuals and directors as appropriate and necessary even where companies may no longer be operating," she said.
The company is accused of mapping the behaviour of voters in the run-up to the 2016 US election and European Union (EU) referendum. The company also allegedly did election-related work in India for the Congress and JD(U) parties, according to revelations by former CA employee turned whistleblower Christopher Wylie.
Damian Collins, chair of the House of Commons select committee for Digital, Culture, Media and Sport (DCMS) which is conducting its own investigation as part of a wider inquiry in fake news, said: "Cambridge Analytica and (parent company) SCL Group cannot be allowed to delete their data history by closing."
"The investigations into their work are vital," Collins said.
He said the committee is determined to ensure that the closure is not an attempt to "run and hide" and that the companies are not closing down to try to avoid them being rigorously investigated over the allegations that are being made against them.
Earlier in the week, Collins repeated a request for Facebook chief Mark Zuckerberg to appear before the committee, saying evidence provided by the company's chief technology officer Mike Schroepfer last week "failed to answer fully" MPs' questions.
In a firmly worded letter to Facebook's public policy chief, Rebecca Stimson, he said: "We hope that he (Zuckerberg) will respond positively to our request, but if not the Committee will resolve to issue a formal summons for him to appear when he is next in the UK.
Facebook has apologised to users for a "breach of trust" and claims to have tightened its privacy restrictions.
Cambridge Analytica yesterday said it had been the subject of "numerous unfounded accusations" and had been "vilified" for activities that were both legal and accepted as a "standard component of online advertising in both the political and commercial arenas".
It blamed a "siege of media coverage" for driving away customers, meaning the company's continued operation was no longer viable, leaving it "with no realistic alternative to placing the company into administration".
The company said that its parent company, SCL Elections, would also be commencing bankruptcy proceedings.
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