With regards to breathing and body position we are not given quite so many opportunities as the arms, which we will move onto next since these key skills need full body accuracy. Taking something away here will not have the same effect. Perhaps, as already mentioned, the single most effective movement is the torpedo drill.
Torpedo drill: Swim front crawl with the arms by the side. If the kick is good and the core movements at the hips are effective, then you should be able to drive the rotation so the upper body gets onto its side without the arms being used. If this is possible you then stop using the arms as stabilisers. This allows them to pull effectively rather than stop the body rolling into backstroke or lifting the head into a breath.