Don't know what antibody test the Oxford/ONS study is using. However, all test have false negative and false positive results.
If you want to check your antibodies this can be done commercially via a simple finger prick test.
The standard Roche (Anti-SARS-CoV-2 N) test only looks at antibodies from infection, so isn't of any use if looking at AB response from vaccination. If you want to know your response to vaccination, the test you need to do is the Roche (Anti-SARS-COV-2 S) test which reports antibody level in U/mL.
This is about £50 and can be ordered from here:
https://www.testingforall.org/product/covid-19-immunity-tracker/Did mine last week as I work in a V high risk environment. Nice to know I've got AB's, won't change my precautions, but does takes away some of my day to day anxiety.