With the Reformation sweeping its way through much of Northern Europe and the German states, is it inevitable that England would've been hit by the changing of ideas?
Did the relationship between England and Rome have other issues before the Pope denied Henry VIII's wish of having his marriage to Catherine of Aragon annulled?
Were the populace of England already showing discontent towards Catholicism and was the changing of power away from the Pope a popular view, or was it solely instigated by Henry VIII and his government?
Finally as a sub-question, how was England viewed during the War of the Roses by Rome, and how was Catholicism treated by the Yorkists and Lancastrians?
On the whole, 'inevitable' isn't a great way of thinking about history - most historians tend to view that kind of word with no small amount of scepticism, which isn't all that surprising, I think. 'Inevitable' implies a forgone conclusion - a predictable set of specific events. In retrospect, it often seems like an event could only end one way, but obviously that isn't ever really accurate. Think in terms of 'likelihood' instead - i.e. what seemed probable, based on context. Sorry - enough of semantics.
Thinking about whether England's break from the Catholic Church was 'very likely' following the War of the Roses is actually quite complex, and calls for a certain amount of speculation, given the hypothetical nature of the question. There's evidence for both sides of the debate.
On the 'for side': the ideology of Luther's reformation was moving through Europe by the 1530s, and Luther's three 1520 texts, To the Christian Nobility, On the Babylonian Captivity of the Church, and On the Freedom of a Christian, had circulated to no small extent. Anticlericalism in Europe in general was fairly widespread - in England specifically, think about Lollardy and John Wycliffe in the 14th century, or the criticisms that Chaucer's Canterbury Tales makes quite clear, regarding Church abuses, sale of indulgences, hypocrisy, etc. If you're of the opinion that the people were the driving force for religious change, then it's certainly quite possible that a popular movement appealing directly to the people (Luther writing in vernacular, using printing press to disseminate images for a largely illiterate audience, etc.) would have found feet in England and pushed the change.
If you prefer the 'reformation from above' idea, then there's a lot to suggest that Henry VIII might have adopted a Protestant-esque religion in England simply for the massive political and economic benefits of the break with Rome - I won't go into too much detail here, given that his reasons are well discussed generally, but consider these factors - splitting with the papacy in Rome allowed Henry to keep tithes in England, repossess and sell Church lands in Britain, consolidate secular and religious power in a single authority, reduce external interference in the state, and acquire a divorce in order to secure a stable succession. With that level of benefit, it does seem probable that the break with Rome - already happening elsewhere in Europe - might have offered a pretty attractive set of reasons, regardless of anything else.
On the against side (that is, the 'not inevitable' side), there's evidence to show that it might not have happened, had events transpired in another way. I stress that this is speculative, given that we know the way that events did transpire - but it is at least based on evidence.
Henry VIII wasn't a Protestant. In the early 1520s, shortly after the publication and circulation of Luther's texts, Henry wrote (or had written) Defence of the Seven Sacraments against the new and emerging religious ideas - for which he was awarded the title 'Defender of the Faith' from the pope himself. So - we move from 'inevitable' into murkier territories - Henry, of course, might have ended up resisting Protestantism in the same way that Charles V attempted to.
For my own two cents - I think that religious change in England was highly probable prior to the actual split. The political climate was already changing, with the centralisation of power increasing, and the institutions of government becoming more defined. Ousting an external influence like the papacy in Rome allowed Henry VIII to increase his secular authority to a new level.
Of course - there's always an argument to be made that Henry really was responding to a corrupt Church; one that had steadily become more and more incompatible with his, and England's, religious beliefs.