Time off for dependants is the legal right under section 57A of the Employment Rights Act 1996 to take reasonable, unpaid time off work to deal with an emergency involving a dependant, such as a sudden illness, injury, or death.
It’s meant to cover the immediate, practical crisis, not the wider period of care or grieving that follows, and tribunals have generally treated “reasonable” as a day or two rather than a week or more.
In practice
If your aunt has a fall and you need a day to get her to hospital and arrange care, that's the kind of practical emergency this right covers, not the days after when you're just checking in on her.
See also
Legislation covered