After searching for a while I was unable to find anything relating to this error and the VDP 5.5.5 Admin Guide doesn't mention the fix. I assumed it would be a permission problem so I added the vCenter service account to the local administrators group to ensure it had full access to SQL. This didn't resolve the issue, I then checked the Backup Agent service which was running as the Local System user and realised that it obviously didn't have permission to SQL. I changed this account to run as the vCenter service account and then created the backup job again and hey presto:
I removed the vCenter service account from the local administrators group and added it to a global SQL administrators group just to tidy things up. Remember this is my lab environment so I'm comfortable with the vCenter service account having those permissions.
Update - 23/04/2014
The VDP 5.5.5 Admin Guide does actually advise you regarding this issue on Page 145 as this is applicable to SQL 2012: