Hi Annette,
Your doctor is right, I think. 6.5mmol/l is a high fasting blood sugar reading, although still within the normal range.
One of the definitions of diabetes is a fasting level of 7 or over. A healthy non-diabetic will typically be below 5.
Now, the good news. You can lower your fasting level very quickly, and greatly reduce your risk of developing diabetes as a result.
You need to follow a diet that reduces the demand for insulin. Your 6.5 score shows that your body is trying but failing to dispose of the sugars in your blood. Give it a hand by consuming foods that don't contain sugar and aren't metabolised into sugar, lowering the need to produce so much insulin.
In brief, try to cut out breads, pasta, rice and potatoes, as well as the more obvious sources of sugar i.e. biscuits, cakes etc. Replace these things with vegetables, meat, fish, eggs, cheese, butter, cream, nuts etc.
If you can do this, I think your next fasting level should be a great deal better.
All the best,
fergusc