The NICE guidance, which your NHS GP should be following, is here: http://www.nice.org.uk/guidance/cg181
Your GP should have used more information than just your non-HDL results; they should have given you a standardised risk assessment call QRISK2.
http://www.nhs.uk/news/2014/02February/Pages/NICE-publishes-...
That risk assessment needs to know your age, sex, BMI, ethnicity, family history, your blood pressure, your blood cholesterol levels, and whether you have history of diabetes, high blood pressure, atrial fibrillation, or rheumatoid arthritis.
Your GP should have most of that, and if you think they don't it's probably a good idea to let them know.
You've said that you think the "eating saturated fat leads to high blood cholesterol" thing is wrong, and that the NHS seems to push this, but you also say that your GP didn't ask you what you eat, so it seems your GP isn't pushing that hypothesis. Your GP (from what you've said) didn't say "stop eating animal fat and take this medication", your GP said "take this medication".