Thousands of Morrisons staff are suing the company after their personal details were posted on the internet.
The High Court action is seeking to make the supermarket chain liable after a member of staff stole the data of nearly 100,000 employees in 2014.
Andrew Skelton, an auditor at the firm's Bradford head office, was jailed for eight years in 2015.
The workers are claiming compensation for the "upset and distress" caused but Morrisons denies liability.
Jonathan Barnes, counsel for 5,518 former and current Morrisons employees, told Mr Justice Langstaff in London the company had already been awarded £170,000 compensation against Skelton.
He added that the trial judge said Skelton wanted to do the company "some real damage".
"The judge was sure that the employees were victims too, and it is those victims who have received no compensation for their distress or loss of control of the situation," Mr Barnes said.
He said it was a "simple complaint" by the employees who were required to provide the information when they joined Morrisons.
"We say that, having entrusted the information to Morrisons, we should now be compensated for the upset and distress caused by what we say was a failure to keep safe that information," Mr Barnes told the judge.
During his trial at Bradford Crown Court, the jury heard Skelton's motive for the data theft appeared to have been a grudge over a previous incident where he was accused of dealing in legal highs at work.
The employees claim the leak exposed them to the risk of identity theft and potential financial loss and Morrisons is responsible for breaches of privacy, confidence and data protection laws.
The trial, which is concerned only with liability, is due to last two weeks.