Firstly update the your repositories replacing with “breezy” with “dapper” for example. You can work out the release names and additionally even change the URL’s to a closer mirrors by referring to the official repository list. This can be done using:

vi /etc/apt/sources.list

If you’re not familiar with vi, ESC leaves editing mode and INS enters editting mode. To save and quit when not in editing mode use:

:wq

To update the sources list then upgrade your distribution use the following commands after each other:

apt-get update
apt-get dist-upgrade

Double check the the upgrade using:

apt-get -f install

Then reboot to make all your upgrades take effect:

shutdown -r now

Using the following command will then confirm your server’s version:

lsb_release -a

Update!

I’ve since found out the method above is not the recommended process for upgrading please refer to the preferred process using update-manager-core. Additionally the process I used above has been officially documented on the Ubuntu help site.