US-based boffin Professor David Carroll (of the Parsons School of Design in New York) had filed a subject access request (SAR) in the United Kingdom, because American law didn't give him any way to get Cambridge Analytica's owner to disgorge the information it holds about him.
The ICO issued the order on Friday, giving the organisation 30 days to comply, saying it was a "criminal offence" if it went ignored.
Facebook's failure to compel Cambridge Analytica to delete the data it had illegally connected meant that the company was able to use the data during the election itself.
Cambridge Analytica announced on Wednesday it plans to file for bankruptcy in Britain and the US.
The ICO noted that even non-British citizens have the right to seek and obtain data held by a British firm.More news: Tough win for Jason Day
Over the past several months, Cambridge Analytica has been the subject of numerous unfounded accusations and, despite the Company's efforts to correct the record, has been vilified for activities that are not only legal, but also widely accepted as a standard component of online advertising in both the political and commercial arenas.
Carroll requested his data back in September 2017, before the most recent Facebook controversy, but wasn't happy with what he got back.
In doing so, the Information Commissioner's Office (ICO) has set a precedent for how Cambridge Analytica and other firms would have to deal with illegally collected information, potentially allowing millions of other U.S. Facebook users to demand information on exactly what data companies have on them.
The row over the improper use of data on 87 million Facebook users by Cambridge Analytica in President Donald Trump's 2016 USA election campaign, has hurt the shares of the world's biggest social network and prompted multiple official investigations.
Information Commissioner Elizabeth Denham said the company "has consistently refused to cooperate with our investigation".