Lord Emslie, the judge at the Court of Session in Edinburgh, has allowed the case to go ahead, and the PRS is asking for damages of £200,000.
The organisation claims that staff should pay royalties because they take radios into work where other people can hear them.
"If copyright music is being played in public - in shops, restaurants, workplaces or any other business - clearance is needed to do so from the owners of that music," said the PRS in a statement.
"Some 92 per cent of PRS members earn less than £10,000 a year from PRS royalties so the income from unlicensed use is important to them.
"Kwik Fit has been given every opportunity to take out the appropriate licences but has refused. Court action is regrettable but Kwik Fit's actions have left us with no choice."
The PRS filed over 200 complaints that radios were being played audibly. But Kwik Fit responded by saying that it did not allow radios to be used at work.
Lord Emslie said in his ruling: "The key point to note, it was said, was that the findings on each occasion were the same with music audibly 'blaring' from employees' radios in such circumstances that [Kwik Fit's] local and central management could not have failed to be aware of what was going on.
"The allegations are of a widespread and consistent picture emerging over many years whereby routine copyright infringement in the workplace was, or inferentially must have been, known to and 'authorised' or 'permitted' by local and central management."
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