Andrew, I can only echo what the other guys have posted so far, not that I've got an ATPL or anything. But one thing I will say, having finished school only a couple of years ago (on the right side of the border though
) we have a non calculator exam paper in our 5th year (Highers) and it is the best thing I ever did with respect to my mental arithmetic. I'm not sure what the position is with your exams for GCSE/A levels etc. In school, try to use your calculator as little as possible, even if it means taking a couple of mins longer to complete a question. The people who have already replied are bang on when they say you'll be surprised how quickly things improve. I hardly touched a calculator through my final 2 years at school except where it was strictly necessary. For school maths/physics questions the numbers tend to be fixed to give a nice result, so rather than reaching for the calculator every time sine, cosine etc appear for example, learn the common values and do the maths in your head. You will improve rapidly. Like Notso said, it's something which is within your control to remedy, do something about it while you still have opportunity to practise on a regular basis in school. It'll help no end.
Stick in and all the best with the exams.