I think change always stresses the body and that's why it's not a good idea to start both together.

If you are eating rubbish then you won't be fit enough for exercise.

I think start a good diet so that you detox and then after you've lost some weight start exercise - gradually - strengthen the heart and blood vessels and get the lungs working properly slowly before building up to a more demanding routine.

This was the way forward my trainer put forward and it worked for me.