In general, your workplace can (assuming that you have agreed to this in policy) ensure that you're using your computer for approved uses, and it can access all work-related information on the computer. You do have (limited) privacy over anything personal on the computer, but they're welcome to discipline or fire you just for its existence, and in some cases they may access it if they have reasonable belief that they have to.
This ruling clarifies that if your personal information is mixed in with professional information, the company may access it, as little as necessary (the word you'll come across lots is "proportionate"), as part of an internal investigation or similar. This has been spelled out by at least the British Government for a while now, nothing has changed.
EDIT: On a side note, anyone else notice how the article names the ex-employee and not the employer?