I am feeling very anxious all the time, but know of no reason why I should be. Is this normal?

Generally speaking, it is not normal to feel anxious all the time. 

For those who suffer with an anxiety disorder or a physical condition of which anxiety is a symptom (e.g. overactive Thyroid) it is sadly more common.  

If you cannot identify a cause for your anxiety in your day to day life, we would recommend seeing your GP to rule out any medical reasons for your condition.