I will try to put it in context. 6.8 is not a terribly high reading but it is an indication that something is wrong. It is asking too much of a person to tell them this sort of information and then say that they shouldn't worry. To put it another way, if the NHS really didn't want you to worry they shouldn't have mentioned it.
How much should you worry?
Something caused you to arrive at this point and if you do nothing then, according to the NHS, it will get progressively worse with time. There is the means to slow this progression. Many think you can stop it from getting any worse and a few say the situation can be reversed although I wouldn't bet money on the last one.
You had a slightly high sugar reading and presumably you have had many more that you didn't know about. In order to find out more you could test your blood sugar yourself occasionally to see if any particular foods are causing the "highs". Many of us do just that and we rearrange our food menu to eat less of the troublesome foods that we identify and some people cut them out altogether.
The word diet is used a lot when dealing with diabetes. This does not have the word "slimming" in front of it but refers to your general eating habits. If, however, you are overweight then losing some of it can be beneficial.
High blood sugar readings damage your body and only eating foods that don't raise your blood sugar too much seems like a good idea.