There's nothing in your post, Emmie, about your income.
Housing Benefit and Council Tax Reduction are both available to people who've got low incomes (irrespective of whether that's because they're on things like Job Seeker's allowance or just because they don't earn much or get much from their pensions). To qualify they usually need to have savings of less than £16,000 (but the amount they get will probably start to reduce if their savings are over £5000).
Housing Benefit is a national scheme but there are regional differences in the amounts that can be paid (based upon typical costs of renting across different areas, rather than individual council policies). So people living in central London can receive more than those in, say, Tyneside, simply because rents are so much higher in London.
The basic rules about Council Tax Reduction are set nationally but it's up to individual councils to decide the maximum discounts which can be applied in their areas.