This varies by area.
I tend to get mine from my GP practice, because I have online access to my GP records, so I can see it when the result comes in, which is usually half a day later (same day if I do blood test in morning).
If I get it from the hospital, I have to call and ask the CNS, and I'm not sure they're still around (redeployed to covid-19), so I ignore the hospital blood test forms and get one from my GP.
I did once edit the hospital form and added my GP as a secondary report, and that worked, and it appeared in my GP record. Neither the hospital nor GP can see any blood test result they didn't order, unless they are filled in as a secondary report. Once I had blood test forms from both of them for different things, and just a single phile of blood was collected, but they each only got the result for the tests they asked for.