Cycle faster, harder and longer: it sounds like you are simply not exerting yourself as intensely when cycling. Cycling is one of the most energetically efficient ways of moving, so you need to really push to get a workout. Try finding some long hills (the steeper the better), or maintain 40kph for as long as possible. Either of these should get your heart and lungs working.

 Trust me, short of freewheeling down a hill, cycling will give both your muscles and your cardiovascular system a workout. I don't know who gave you that idea.

If you don't believe me, sit quietly by your bike and relax for 10 minutes. Then take your pulse. Now get on your bike and pedal gently round the block for about 10 minutes. Nothing strenuous. Now take your pulse again. You will find that your pulse rate (and rate of breathing, if you had bothered to measure that as well) has increased.

This is a measure of the workout you got. Unless you are very un-fit it will not be much of a workout, any more than if you had just walked or jogged slowly, but just as a strenuous run gives you more of a workout than a paralytic jog, so a really strenuous bout of cycling can leave you on all fours, barking at ants. The only limit is how hard you cycle. This is true in much the same way as for running.