I have read that when doing cardio, the first 20mins is just using up your bodys energy and only after 20mins do you start burning the fat. Is this true? this obviously depends on the intensity of the cardio?

Also, what are the best exercises to do in the gym to burn calories? bike, treadmill, cross trainer etc?

 Thanks.

Everyone keeps talking about how good intervals are for losing weight.  I guess it's true?

There's not a lot of difference between the different machines, the intensity at which you do them will make the biggest difference.  Intervals are the most time efficient way to get an intense calorie burning workout in a short period of time.

That is true to a certain extent - you do have to burn up your body's calorie reserves first.  Longer workouts are good, but if you have less time, think about intervals.  More bang for your buck.

Are intervals what we do in my spin class?  slower and then faster?

longer workouts seem better to me - by the time i've gone to the gym, got changed and so on, it hardly seems worth it for 20 mins.

I'm sure there are metabolic differences, but who knows what food will affect you as an individual?

After 30 minutes to 35 minutes you "start burning fat". Spinning is the most consuming exercise without any doubt.
If you want to know how many calories you are burning I have created this calorie burning calculator. you need to select the activity and input for how many minnutes you did it. This will tell you how many calories you burned.
You will fin this calculator in http://www.sixpack-exercises.com/fat-burned-calculator.html

Cheers,