A glitch in the system let customers who input a tracking number access the details attached to other tracking numbers.
According to the BBC, the Information Commissioners Office plans to investigate the breach.
A spokesman for Parcelforce Worldwide apologised for the error: "We can confirm that the fault was rectified and the service restored on Thursday night. We apologise to customers for any inconvenience caused", he told the BBC.
The company claimed that the issue began after maintenance work was completed on Wednesday night. Parcelforce Worldwide claims to be able to deliver to 99.6% of the world's population.