I think you're getting loads of duff advice here OP (GeoffreyGeoffrey I don't mean yours). It sounds as though the property you were residing in was not on the Council Tax Valuation List. The first thing to do is check with the Valuation Office Agency to find out when it was brought onto the valuation list. This is a national list, and properties are added and removed all the time.
www.tax.service.gov.uk/valuation-office-agency-contact-frontend/about-council-tax
It's not up to the Council to decide if a property is included in the list, it's down to the Valuation Office Agency. Once it's in the list it's down to the local Council to collect the tax on it.
It may be the fault of your Employer if they failed to let the Council or the Valuation Office Agency know that there were residents in the property. Someone moving in to some properties means it must be split - it then becomes part business rates and part council tax.
You have the right to appeal against being included in the valuation list if you think it's inaccurate (although it sounds as though yours should have been). If you check here
www.gov.uk/council-tax-bands
or you can ring the VOA on 03000 501 501 and they can check it for you. They should also be able to tell you how they were notified if it's literally only gone back to the date you moved into the property.
You can find out exactly when the property was brought onto the list (this is called the effective date). If the date you can see is earlier than the start date of the charge on the bill then someone will definitely have been receiving bills. If the date is the same as the start date on the bill then it's just been discovered that it should have been chargeable for council tax.
In either of these scenarios, technically as the resident you are liable. However you should look into the Council's complaints procedure. In the meantime you should make an arrangement to pay a minimal amount. You should make a complaint about the length of time it's taken for the Council to find out that there should have been a charge (or a charge to you). Once they've turned you down (which they usually do) you can then complain to the Local Government and Social Care Ombudsman.
www.lgo.org.uk/make-a-complaint/fact-sheets/benefits-and-tax/council-tax
Don't think this is a waste of time - the chances of success with the Ombudsman are far greater than with a complaint to the Council. However when you make your complaint you should include that you will be taking it to the Ombudsman if they don't write off the debt. Also please bear in mind that the legislation doesn't actually say there is a requirement for you offer yourself as a taxpayer, the onus is on the council to request the information from you, and it should have been done in writing.
In the olden days when I worked in Council Tax we had teams of inspectors who would check most properties over a two year period. Sadly with the cuts that have been made the majority of those jobs have gone, which is why it won't have been picked up. The fact that you get post there or deal with other council departments makes no difference - they don't share information about residents due to data protection (unless there is consent to do so).
It all sounds much more scary than it actually is, please feel free to message me if you need any help with this. Good luck!