Should I cycle? Yes! Sure you should!
5 Fs why cycling is a good idea:

Fitness

Regular cycling can reduce obesity and the risk of heart disease. Even less frequent cycling for short journeys constitutes more exercise than driving a car! It helps to maintain healthy joints and muscle tone without the risks associated with high impact sports such as jogging.

Contact with your immediate surroundings - the wind on your face - can help to reduce stress levels and keep your reactions and brain alert. According to the BMA, the health benefits of cycling outweigh the accident risks by a factor of 20:1 (and that can be reduced further by taking professional cycling training!).