When you break with Rome, you don't just jump ship to the biggest "alternative" - that would be the perfect way to prove that your belief is insincere, since you have suddenly switched to a religion which bears few similarities to your culture or understanding of Christianity - if you're willing to compromise on your doctrinal beliefs just to break with Rome then you're clearly not a very good Christian. Perhaps if your state bordered an Orthodox country then you could as the cultures would be much closer and so points of doctrine would be closer to Orthodox (as some doctrinal beliefs tend to slowly change across geographical regions in the same way language changes as you travel further and further) but for England, there's no shared system of belief beyond the basic aspects of Christianity. It wouldn't be that far flung from England changing to Islam just to spite the Pope - and I know that supposedly Richard II did consider this, but seriously, does anyone actually believe that the rest of England wouldn't have instantly overthrown him and then horribly lynched and butchered him as a heretic for doing this?
No, if England were to break from Rome it would form its own Church based around English cultural mores and various church practises which existed in England and not in Rome.
Prior to 1066 the English Church already diverged from the Roman Church in matters such as Simony and Priests marrying. Papal support for the Norman invasion was in large part an attempt to rein in this far to independently minded Church and assert Papal supremacy. If the invasion had failed it's not that unlikely that England would throw it's weight behind Constantinople, this not being long after the Great Schism. This would be a political and diplomatic act, not theological. Only in the centuries to come would this mean that the English Church would be seen as 'Orthodox'.
Also remember that both the Catholic and Orthodox Churches consider themselves to be The Catholic Orthodox Church