There is no council tax to pay where ALL the adults aged 18 or over in the household are full time students. The University provides details of all full time students to the local council tax office for the purposes of exemption from council tax.
If you live outside the Lancaster area and need to obtain an exemption certificate you should contact the Student Registry in University House who will supply proof of your full time student status for the purposes of council tax. Please note the council tax office will not accept evidence from any other source (such as your academic department).
If you study part-time you will not be exempt under the student rules. However, you may be entitled to Council Tax Benefit if you have a low income, and/or to a 25% discount if you live alone.
As a part-time student you will be paying reduced fees and will not be eligible for a Council Tax exemption certificate from the University.
There's more information on the Lancaster City Council website.