Lets assume Edward makes it into his 30s although he does not have any legitimate children. What effect would this have on British and European history.
Edward VI's survival into adulthood would have cemented the supremacy of the Book of Common Prayer and (very early) Anglicanism. The absence of Mary Queen of Scots would have hastened the end of the tug-of-war between Catholicism and the newly growing Protestant movement. Edward's personal take on Christian theology and liturgy wouldn't have mattered as much as Cramner and Bucer's growing hold on the direction of the state church. The Elizabethan religious settlement would have been avoided. Even if an ER analogue had to force a compromise between more Protestant and more Catholic camps, he/she would likely have had an easier time if a mature Edward VI (via important reformers) had time to solidify Protestant doctrine and remove more remnants of Catholicism.
There is always the chance that a later death of Edward VI (without legit heirs) could have lifted a Catholic to the throne again. Heck, this happened even OTL with James, for example. Again, an earlier definition and enforcement of Anglicanism would have made the re-conversion of England quite difficult. A Catholic monarch who could hold the throne might forge greater ties with the Hapsburgs and the Bourbons. I suspect that by this time the English would have already developed a hostility towards Catholicism as a "foreign religion" and a religion that implies abetting foreign powers. I would not expect re-conversion of England. I would expect great resentment among many nobles and commoners alike, and a perilous situation for recusant Catholics (especially recusant nobles, who would be branded as 'traitors').