Which council for which service, service by service

District, borough or city

Rubbish collection and recycling. Council Tax collection. Housing, including the council's own stock and homelessness duties. Planning applications for households and most businesses.

In practice districts also commonly hold environmental health, licensing, car parks, leisure centres and elections administration, which are the things residents interact with most often.

County

Education. Transport, as the highway authority. Planning, meaning the development plan and minerals and waste. Fire and public safety. Social care for adults and children. Libraries. Waste disposal. Trading standards.

These are the large statutory functions, and they usually have their own dedicated reporting routes, which are much faster than a general enquiry form.

The four most misdirected

Potholes. County, always, in a two-tier area. The road outside your house feels like the most local thing there is and it is an upper-tier responsibility.

School admissions and appeals. County, not the school, and not the district.

Trading standards. County. It is looked for at the district constantly and has never sat there.

Social care. County. Confused with housing, which is the district, because both are about where somebody lives.

Not the council at all

Fire, police and public transport. gov.uk notes that in single-tier areas these are provided through joint authorities, and the same is broadly true in two-tier areas.

Police goes to the force and its commissioner. Fire goes to the fire authority. Buses are largely commercial, with the council or a combined authority responsible for planning and supported services rather than for running them.