The effect of no Luther on the Church of England.
Well here's the thing. In terms of doctrine, the newly established Church of England remained largely Catholic. The whole purpose of the split was to free Henry from Papal authority and allow him to divorce his wife. I believe his legal justification for splitting went something along the lines of "King Arturh was totally real, and he proclaimed Britain an Empire, and as his successor that means I am an Emperor, and therefore not beholden to foreign power". It wasn't until his son Edward took the throne that more radical Protestant doctrine began to be incorporated.
The way I see it there are two main factors that will influence whether or not Henry breaks from Rome. The first is the weakening of Papal authority brought about by the reformation that allows this sort of action to be on the cards.
Second, there is the fact that at the time the current Pope was in the "custody" of Charles V of the HRE, who was a close relative of Catherine of Aragon, and therefore unlikley to allow the Pope to grant Henry a divorce. The thing is, however, the reason he ended up in custody, at least as far as I know, was due to the fact that Rome had recently been sacked by the disgruntled Imperial soldiers who Charles had sent to garrison Rome, many of whom were of Protestant sympathies.
If removing Luther butterflies, or at least delays, the chaos of the reformation, then it is less likely that Rome gets sacked, and therefore Henry is in a better position to negotiate with the Pope for a divorce, and therefore won't be as likely to break with Rome (although the opportunity to loot the monasteries might make him reconsider). If, on the other hand, removing Luther doesn't prevent the reformation then it's the same conditions as OTL.