King John the Much Maligned actually did resist admirably to the Papal pressure, and, more importantly, England backed him up to the hilt; the Papal Interdict of 1208 is probably one of the best examples showing that although medieval people were deeply religious they didn't actually care all that much about the Church with capital C and its hierarchy.
The context is that the Pope of that time, Innocent III, consecrated Stephen Langton as Archbishop of Canterbury (and head of the Church hierarchy in England) without the King's consent; the regular procedure was that the King would propose a candidate (or a short list of candidates) and the Pope would confirm and consecrate the candidate (or pick one of the list); in case of disagreement it was expected that the King and the Pope would negotiate. That the Pope consecrated a head of the English church without Royal consent was a hostile move; the King responded by refusing to allow Stephen Langton to enter the country, and, for good measure, seized the lands of the archbishopric. The Pope escalated the conflict by placing the kingdom under the Interdict.
The Interdict, in the mind of the Pope, was the ultimate deterrent, the nuclear option as we would say. In principle, priests were prohibited to perform any religious service other than the baptism of the young children and the confession and absolution of the dying. No Mass was to be celebrated, no communion, no confession, and most importantly, no marriages could take place. This would put the country under enormous pressure, hoped the Pope, and the King would have no choice but to submit. What happened in reality was quite different.
Essentially, both King John personally and England collectively chose to ignore the Interdict. Churches remained open, marriages were celebrated, life continued as before; those priests who manifested excessive obedience to the Pope and tried to enforce the Interdict found that life had become quite hard: their lands were seized (as were the lands administered in the benefit of the Papal See itself), they were driven out of the country, their mistresses were arrested and held until the sinful priest payed a hefty fine.
Seeing that placing an Interdict on England was one thing, but having it enforced was quite another, Pope Innocent excommunicated King John (in 1209), with no effect other than (a) determining the King to consider seriously the possibility of a war against the Pope and (b) reinforcing the King's determination to redirect the revenues of the Church; Wikipedia says that "around 14% of annual income from the English church was being appropriated by John each year". The King's revenues increased, the country carried on as before: what's not to like. And the King and the Kingdom continued in this happy state until 1213, when a compromise with the Pope was sought.
The issue was King Philip II of France, Philip Auguste as the French call him. King Philip saw the excommunication of King John as a very convenient pretext for going to war against England, and was busy building a fleet and gathering an army; whether he had the consent of the Pope of not is not clear, but he definitely did not have any material support from the Pope. King John performed an admirable show of contrition, declared himself a humble vassal of the Pope and agreed to pay annual tribute -- which was about one tenth of the annual income he had collected from the lands of the Church during the years of the Interdict, and which both parties tacitly forgot after three or four years anyway; in exchange, he got the Pope to allow him to make war upon France.
And here comes the actual interesting point where history did truly lay balanced on a fine point; for John's campaign proceeded quite well initially, or at least not worse than any other medieval military campaign, despite the growing reluctance of the English lords to support John in foreign adventures; the English took Anjou; their ally Emperor Otto IV of the Holy Roman Empire attacked from the north. All seemed to go so well.
But then came emperor Otto's defeat at Bouvines (today on the border between France and Belgium, at that time in Flanders), which in the real history ended all hope of restoration of the Angevin Empire, sealed the fate of King John (who not only acquired the nickname Lackland for losing many of the possessions on the mainland, but also ran out of money and had to accept to sign the Magna Carta), and launched France on its way towards becoming a superbly centralized state (which it still is).
But the outcome of the battle of Bouvines was not preset; on the contrary, it is believed that the Allies (the Holy Roman Emperor, England, Boulogne and Flanders) had the advantage of numbers. The fortunes of the battle fluctuated during the day; at one point King Philip himself was "unhorsed and narrowly escaped death" (words from the Wikipedia article). In the real history the French won and the Allies lost. But if Philip had been killed or taken prisoner, if William Longespée ("Longsword") had succeeded in taking the bridge instead of being taken prisoner, history would have been different. The English crown would have kept the Angevin lands (Normandy, Brittany, Anjou, Touraine), would have kept Aquitaine -- about the one third of France! France would be much smaller, while England would be just one of the provinces of an Empire spanning the Channel.