In order to ensure that your Internet Explorer can run the latest version of Java, you must be running IE 11.0.9600.18230 or higher. For information on how to check your version number, see article here.
It may be possible that your user account may not have access rights to be able to update Java. If this is the case, then you may need to contact your ICT department and request that they update Java for you.
1. Head to http://www.java.com/en/download and click the 'Agree and Proceed' button
2. Click the 'Free Java Download' button in as seen in the image below.
3. You will now see the text on the button has changed to 'Agree and Start Free Download'. Click the button again
4. In the security prompt box that appears at the bottom of the screen (see below) click the 'Save' button
5. Once the file has downloaded, click 'Run' to run the installer
6. The Java Setup wizard will now launch. Run through the installer and complete the installation. The wizard may try to uninstall previous versions, if this happens, allow it to uninstall all the old instances and carry on with the rest of the install wizard.