What difference, if any, was there between the Christianity first introduced to the British Isles and the pre-schism church?
None. But the pre-schism Church was quite diverse. Different parts of the Church venerated different saints, had different feasts and had different liturgical practices. This was the case both in the Eastern and Western half of the Church. Alexandria didn't celebrate the Byzantine rite, nor did Canterbury celebrate the Roman rite.
If there was no difference at all, what caused the East to stand back after the schism and allow Britain to fall to Rome?
You assume that the Easterners knew or even cared about Britain.
From what I've read, between the schism and the Norman invasion, the Church in England was hardly "in line" with Rome, some kings were ex-communicated and such.
Same thing with the Holy Roman Empire and the Normans in Southern Italy. Quite often those excommunications had to do with the investiture controversy, politics or the maltreatment of the clergy. That kings were excommunicated by the Pope doesn't automatically mean that the churches in their domains weren't doctrinally in line with Rome.
Did the Orthodox do much to go to Britain and say "hey guys, we're your "ancestors", and while you disagree with Rome, maybe you'd see truth with us?"
No. Besides, they had other things to worry about, like the Turkish onslaught that followed a few years after the schism.
At the time the Byzantines thought they could bring the West back into the Church through an agreement with the Pope. Proselytising western nations probably didn't even cross their minds at the time. When the Byzantines found out at the Council of Florence in the 15th century that this approach wasn't going to work they were but a few decades away from being subjected to the Ottoman yoke. From that time onwards keeping their own people Orthodox and preventing them from apostisizing to Islam kept them too busy to even think about sending missionaries to the west.
Lastly, if not, why not? How different would the make up of the Christian faith be if we had been an Orthodox nation from medieval times?
There's no way that the Church of Britain would have been able to have kept communion with the Eastern patriarchates. The distance was too great. Then again, all of Britain's continental neighbours were Roman Catholic and the Archbishops of York and Canterbury traditionally received the pallium from the Roman Patriarch. I can't imagine medieval English kings being too concerned about the doctrinal differences between Orthodoxy and Roman Catholicism either.
The impact on North America (and the growth of protestantism) could have been unfathomable.
I don't know. The Orthodox nations had their fair share of heresies as well. Bogomilism, monothelitism, old believers, etc. We can't really know what would have happened with the Reformation if the schism wouldn't have happened or if England would have maintained communion with the East instead of with Rome.
The changes were subtle and few at the time on the ground realized them. It didn't help that papal supremacy was part of a whole program of reform and restructuring. It's easier to see it in hindsight from our vantage point today than it was to see it happening as it was happening.
The rise of Papal power might not have been a bad thing for the Western church. It rescued it from simony, despotism by feudal rulers and other nasty practices. That doesn't mean that forcing the issue of papal jurisdiction in the East
was a good thing. Quite the contrary, in fact.