Cambridge Analytica's parent company SCL Elections Ltd has been fined £15,000 plus costs for failing to hand over the personal data of a US citizen.
The case was brought by the Information Commissioner's Office (ICO), after a complaint filed by Prof David Carroll, who is a US citizen.
He was one of millions of people whose personal information was harvested from a variety of sources by the company.
SCL admitted it had failed to comply with the ICO's legal notice.
The enforcement notice was issued one day before the firm went into administration last May.
Cambridge Analytica was embroiled in scandal when it emerged that Facebook data collected by UK researcher Dr Aleksandr Kogan via a personality quiz had been shared with it, without consent from users.
There were concerns that some of the data may have been used to target political advertising in the US presidential election and the EU referendum, something Cambridge Analytica denies.
A year before the scandal blew up, Prof Carroll was unhappy about how the political marketing firm was using his data, after it was revealed that it had built profiles on up to 240 million Americans and boasted that it had 4,000 to 5,000 data points on each voter.
In July 2017, Prof Carroll asked the firm to provide him with details of the data it held on him.
Because his data had been processed in the UK, he also filed a complaint with the ICO.
In March the following year, he was sent two files which contained his voter registration information, historical participation in elections and an ideological model of how he might vote in future.
Both Prof Carroll and the ICO felt that SCL was holding back information, with the UK regulator ordering a much fuller disclosure.
SCL ignored this order, forcing the ICO to launch a criminal case against it.
"This has taken two years of complex legal wrangling across two continents. Hopefully this test case will make it easier for others to recover their data," said Prof Carroll in a live stream, posted on Twitter after the case.
"Cambridge Analytica would rather be called criminals and be fined than hand over the data, which I find very strange," he said, adding that there was "more to come".
Another case that he brought in the UK is due to be heard in March.
Paul Bernal, a lecturer in media law at the University of East Anglia, said of the current case: "This is just one small aspect of the bigger problems with Cambridge Analytica. It shouldn't be seen as the end of the story, rather the end of the beginning.
"There's much more to come out, particularly about the role of Facebook, which is ultimately much more important than that of Cambridge Analytica."
The UK's Information Commissioner, Elizabeth Denham, said the prosecution should act as a "warning" to others.
"Organisations that handle personal data must respect people's legal privacy rights. Where that does not happen and companies ignore ICO enforcement notices, we will take action.
"This prosecution, the first against Cambridge Analytica, is a warning that there are consequences for ignoring the law."
It said that its investigation into the firm is continuing.
It has already issued Facebook with a record fine of £500,000 for its role in the Cambridge Analytica scandal, something against which the social network is appealing.