A QR code is just a representation of a string of letters and numbers. Bit like a barcode. This from the government website:
If you give the pharmacy a 'collect code' when you pick up the tests, it helps the NHS match your details to the tests.
It seems to refer just to England.
If you don't have a smartphone, you can just use the string of letters and numbers that the QR code represents. You can get it by calling 119.
test-for-coronavirus.service.gov.uk/collect-lateral-flow-kits
The QR code that you might use when you record the result is a totally different QR code.
Every piece of information you get with the LFT packs tells you to record the result whether it's negative or not. 2 reasons:
The stats that the NHS collects includes the percentage of positive tests against negative tests to allow them to understand the prevalence of the virus.
Also, if nobody bothers to report their negative tests, the NHS doesn't know if you are just stockpiling tests, not bothering to report, or even not reporting positive tests.
So they need to know about negative ones as well. If you order by post, for example, they can trace each individual test back to you. If you pick them up without identification then don't report them, they don't know where those tests have gone.