This is what my local council states about council tax exemptions...
People with Disabilities
If you, or someone who lives with you, need a room, or an extra bathroom or kitchen, or extra space in your property to meet special needs arising from a disability, you may be entitled to a reduced council tax bill.
The bill may be reduced to that of a property in the band immediately below yours. These reductions ensure that disabled people do not pay more tax on account of space needed because of a disability.
For example, if your home is in Band 'A' your bill will be calculated on a 5/9 fraction instead of 6/9.
Other discounts
In addition, certain adults are not counted - they are 'disregarded'. If after 'disregarding' these people, only one adult is counted in your home, you will also get a 25% discount. If after disregarding these people, there are no persons over the age of eighteen then you will get a 50% discount.
What types of people can be disregarded?
The following are groups of people who are not counted for council tax purposes:
18 year olds for whom Child Benefit is payable
Those under 20 who leave full-time education between 1 May and 31 October inclusive
People who are severely mentally impaired (a qualifying benefit such as Attendance Allowance or the middle or high level of the care component of the Disability Living Allowance must be in payment)
People living and being looked after in hospitals and residential care homes
Certain Carers and Care Workers (a qualifying benefit must be in payment such as Attendance Allowance or the highest or middle rate of the care component of the Disability Living Allowance. The person requiring care should not be a spouse partner or child under the age of eighteen, and be cared for at least 35 hours a week on average)
People staying in certain hostels or night shelters
People in prison or bail hostel
Members of religious communities in certain cases
USAF personnel and their non-UK dependents
Members (and dependants) of visiting forces
Persons with diplomatic privilege or immunity
Most full time Students (including DipHe in nursing) The Student must be required to attend the course for periods of at least 24 weeks in the year and be required to study for at least 21 hours per week, on average, when in attendance. Non-British spouses of students are also disregarded provided they do not have recourse to public funds and are prevented from taking paid employment
Hospital based Student Nurses
Youth Trainees aged under 25.
Apprentices training for a NVQ qualification and earning less than £195 per week
I'm not sure if those discounts are statutory or just my council. It's curious that only people with mental impairment are disregarded for council tax purposes.