Oil price has rebounded to near $127 a barrel, led by the bullish heating oil market as China and Europe scramble for barrels, thinning global supply.  US crude for June delivery rose 74 cents to $124.86 a barrel by 0431 GMT, just 1.7 percent below Tuesday's all-time peak of $126.98. New front month July ICE Brent was 97 cents higher at$123.60 a barrel, off an intraday high of $123.71.