When you activate any device on a BES, an IT Policy is pushed to your device as well as the BES-related service books to enable certain features of the handheld.
The IT Policy sets the restrictions on what your device can/can't do as a result of being part of the BES.
So.. there's two parts to your problem.
1. You need to remove the BES service books. That's what the [Desktop] contacts and calendar are. It's fairly simple and can easily be done from the device.
2. You need to remove the IT Policy which is going to be more challenging. You'll need to reset your device back to factory defaults. Don't bother doing #1 because #2 will do it for you.
Use BlackBerry Desktop software and do a FULL backup of your device.
Then see this KB article for removing the IT Policy.
KB14202-How to remove an IT policy from a BlackBerry smartphone
Once you have a factory reset device, you can restore the data you need from your backup. All BES code will be gone now.
The O2 people basically gave you the easy answer, not the correct answer.