Council tax is one of the primary local sources of funds for police, fire, etc. International students and their spouses are exempt (if both are internationals), even if both work. You just have to provide evidence that you are a student, and they will regularly send new bills each Autumn saying you owe money. It doesn’t help that the university can be slow about sending lists of international students to the council so they will automatically consider you exempt. A letter from your college and/or the Student Planning and Assessment office at Durham usually satisfies the council for the student. You will have to pay for the time that you were resident before term starts your first year, this turned out to be about £80 for us for the 2 months we were here.
The harder problem is with spouses. I don’t know if the Durham city finance office has a complete turnover every year in staff, but each year a number of international students regularly get council tax bills for their spouses and you have to haggle sometimes to get them to understand that spouses are exempt. See the bottom of the first page of this helpful form from UKCISA about Council Tax. The main criterion is that you have ‘no recourse to public funds’, which I’m pretty sure almost all US student visas have stamped on them. Just show them this and they should back down about anything.
It is convenient not having to pay and a nice gesture given by the UK gov’t to international students, but one might wish that the council would share this knowledge more widely with their employees. Council Tax bills are good for something…they are just about universally accepted as a proof of address for banks, etc.