The ICO sent a letter of intent to the trust regarding the drive loss in January and has now followed up with the largest Civil Monetary Penalty (CMP) it has ever levied.
At the time on the basis that the issue was caused by a sub-contractor tasked with disposing of 1,000 hard drives in September and October 2010.
Up to 252 of these drives later turned up for sale on eBay, where some of them were later purchased in an unwiped, compromised state by third parties who alerted the trust to the issue.
"The Information Commissioner has ignored our extensive representations," said Brighton and Sussex University Hospitals chief executive, Duncan Selbie in an official statement.
"It is a matter of frank surprise that we still do not know why they have imposed such an extraordinary fine despite repeated attempts to find out, including a freedom of information request which they interestingly refused on the basis that it would 'prejudice the monetary penalty process'," he said.
"We simply cannot afford to pay a £325,000 fine and are therefore appealing to the Information Tribunal."
The ICO said that the Trust had been unable to explain how the contractor given the job of destroying the drives was able to remove such a large number from the hospital building where they were being stored without being detected. The task of disposing of the drives should have been supervised to ensure security.
"The amount of the CMP issued in this case reflects the gravity and scale of the data breach. It sets an example for all organisations - both public and private - of the importance of keeping personal information secure," said ICO deputy commissioner and director of data protection, David Smith.
"That said, patients of the NHS in particular rely on the service to keep their sensitive personal details secure. In this case, the Trust failed significantly in its duty to its patients, and also to its staff."
The problematic dimension of this breach for the ICO will have been the sheer number of hard drives lost and the sensitivity of the data they contained including National Insurance numbers, addresses, and even notes on criminal convictions.
Appealing against fines after making an undertaking is unusual and will be closely watched.
"Organisations need to learn from this and all of the ICO's penalties: data must be encrypted and correctly destroyed, hardware must be kept under lock and key and contractors must be thoroughly vetted to ensure that standards are met," commented ViaSat UK CEO, Chris McIntosh.