The hospital test of 78mmol/mol is a hb1ac, a different test and scale to your meter blood glucose level at 6.4mmol/l. The first is the average of the last three months approximately. The meter you have shows you a level right here and now.
I was 5.4 Before lunch I had 2 pieces of turkey ham slice of roast pork and a salad lettuce cucumber tomatoes peppers celery 1 dessert spoon of mayonnaise and a tangerine
I agree with the posters above your diets may not be as low carb as you think or as low as would give the biggest reductions in numbers. Testing each meal as described by @Rachox would give you a meaningful demonstration of the effect food has on you personally.
5.4 before lunch is excellent. Had you not had the tangerine, your post lunch level would have been better. The rest of the meal was perfect. Perhaps avoid fruit for now, apart from a very few berries with double cream (2 strawberries chopped up, or half a dozen raspberries). Most other fruits are full of sugar and fructose.