Sometimes anxiety is not caused by imagined negative results. Sometimes it is caused by imbalances in the body. A suppressed metabolism could be the cause of anxiety.
For me personally I discovered that allowing myself to remain hungry for too long triggers anxiety. The anxiety has nothing to do with thinking about food. It has to do with the particular hormones my body releases when my body detects insufficient food intake. Having a huge meal makes this anxiety go away quickly.
If you are eating insufficient calories for a long period of time you may end up with elevated cortisol levels. Elevated cortisol levels can make you feel anxious and make your mind race. In this case it is your body giving your mind negative thoughts not your mind causing anxiety.
You must figure out the root cause of anxiety before you can fix it. It is a chicken/egg problem for sure.
Meditation will only fix anxiety caused by the mind. It will not fix anxiety caused by the body.