I don't think you can't convince your GP or any other doctor of this; it's probably not worth your time and you risk alienating your physician. I have a personal policy of mentioning info once to my GP in a very diplomatic way and asking them about their opinion on the topic. Then after that, I drop it. Unfortunately, clinical practice significantly lags behind the current medical literature.

If this were my situation and my doctors were dismissive of my lab test values, I would probably self supplement and maybe use some direct to consumer lab testing. The key is to do enough reading to understand how much to supplement, what forms of the vitamin to supplement, how long to wait to test your levels, and also know if you should be supplementing any other items that are co-factors (I love these topics and enjoy reading about them!!! In my prior job I worked with all kinds of drugs, vitamins and supplements ). Also, another thought is that you are taking in enough B12 from your food, but are not absorbing it due to the other things happening your body. I think supplementing and testing are a great way to figure that out. It's just difficult when you don't have a doctor on your side....

Another alternative (if you have the extra money) is to see a functional medicine doctor. I saw one who looked at my B12 values and immediately started me on supplements. My mainstream medical doctors thought nothing of those same low B12 values in my testing that were originally ordered by them.