So here is the solution:
This project(B) was referencing another project(A) (there are about 10 projects in the solution).
The project it was referencing(A) was making use of Microsoft.AnalysisServices.AdomdClient (as well as a few others) in it's references folder.
To resolve this I added the reference to the project(B) I was working on by adding them from the other project's(A) reference folder, thereby putting them in this projects(B) reference folder.
You will also need to access the properties of the newly added reference (in project B) and set 'Copy Local' to true so that it is added to the project when published, therefore not needing it installed on the target environment as it is now part of the applications setup files.
Hope that makes sense, let me know if you have a similar issue and anything is unclear :)