The NHS relies on heavy triaging - so, for primary care, emergency cases will be seen immediately (either at a hospital or at the nearest GP surgery with an available slot), urgent will be seen same day (at your usual GP surgery), and non-urgent medical problems (eg. back pain that isn't getting worse) might take 2-3 days.

But everything else (eg. discussing blood test results, medication reviews, mental health issues) will get dumped into the "routine" appointment bucket and, yes, will often take 1-2 weeks.

You do hear occasional horror stories about the triage process, but my experience has been pretty reasonable. For example, I lost my voice last year but had no other symptoms - so I expected to have to wait a few days to be seen. But I was treated as an urgent case since it affected my ability to work, and got an appointment that afternoon.