The 25% single-person discount
Council Tax assumes two adults live in a home. If only one adult (aged 18 or over) counts as living there as their main home, you get a 25% discount off the bill. It doesn't matter how much you earn or have saved — this is not means-tested.
You also get the 25% discount if you live with other adults but everyone else is "disregarded" (see below) — so in practice you're treated as the only adult who counts. In England, Wales and Scotland the single-person discount is 25%.
If someone moves out and you're now the only adult, claim the 25% — it isn't applied automatically. Equally, if another adult moves in, tell the council so you're not later asked to repay a discount you no longer qualified for.