You need to let the council know that you have moved in and confirm your student status with them. You can do this by getting your exemption certificate online at www.brighton-hove.gov.uk/counciltax for Brighton and in Eastbourne give your landlord your university student number so they can submit them to the local council for checking against a shared database.
If you are a full time student then you are not liable to pay council tax, but be aware that if someone in your shared house is not a student then they will be liable to pay.