After having a few problems and reading a variety of guides on installing Ubuntu as a guest OS on my Parallels installation on my iMac I finally managed to get there after a suggestion from KevanV on Jaiku.
Go to the Ubuntu website and when you download the ISO ensure you that you check the box which says Check here if you need the alternate desktop CD. This CD does not include the Live CD, instead it uses a text-based installer.
Then when you install Ubuntu ensure you use the text based installer.
Also when asked which screen resolution you wish to use ensure that you check 1024 x 768 only.
Once installed the graphical user interface works just fine.