I agree there is no harm in asking the local council, but I fear you are not going to be able to sway this one. You didn't mention your one day per week learning in the original question but clear 'rules' apply to that as well, I'm afraid, and you need to be classified as a full-time student at an approved college. Most of the 'evidence' to support my answers can be found here.
http://www.direct.gov...tyOrCollege/DG_071488
Now you have also told us that your employer actually owns the house, I'd be inclined to go back there to make your case that the employer should be picking this up. Many years ago as a 5 year-out-of-uni graduate I lived in a house whose tenancy was held by my employer. In it were a mix of full time apprentices, students doing their industrial training plus me - a non-student just using the room Monday through Friday during the week whilst I sold up my house and moved over with Mrs Buildersmate. There never was any question that I would be paying the council tax - it was part of my relocation package.