There seemed to be a small bug in the version of Xamarin Studio where it would fail to create an Android Xamarin.Forms project correctly. When I tried to build the project I got an error “The type or namespace ‘Xamarin’ could not be found”. The issue was reported on the Xamarin forum as well.
It appears that for some reason the Xamarin.Forms package did not download correctly when the project was created. To solve the problem was fairly straight forward as I just needed to grab the Xamarin.Forms package from NuGet, which also pulled down the necessary dependencies for the project.
With the relevant assembly now referenced in the project the project would now build successfully.