As of 15th June 2021, most of the world is on the UK government's "Amber" list. Travellers from these countries arriving in England or Wales are required to enter self-isolation (quarantine) for ten days.
There are various exemptions that apply, but they are almost entirely based on your job or which top-level sporting event you're participating in.
What I can't find is whether there are compassionate exemptions, for example, to be able to visit a dying relative.
There are compassionate exemptions for managed quarantine - not self-isolation, but quarantine in a registered facility - for travellers from "Red" list countries.
Since there are compassionate exemptions for the stricter quarantine, I'd expect to find them for the less strict quarantine - but I'd like to know for sure!