In
How the Catholic Church Built Western Civilization, there's a section describing the study of slag heaps near a particular monastery where the slag had significantly less "wasted metal" than was typical of metallurgy at the time.
The author spun this scenario about how the monks might have been on the verge of discovering some advanced process and how this could have spread throughout the monastic information network across Europe and kicked off the Industrial Revolution centuries early, were it not for Henry's greed.
This article here contains another account, claiming that the monks were about to create a modern blast furnace:
http://www.lewrockwell.com/woods/woods43.html
I think the "early industrial revolution" might be a bit optimistic, but there might be actual technological advances in TTL, in the fields of metallurgy (this particular case) or other areas where the monks were active.
Also, the monastics were the only ones providing education for girls at this time in English history, an area that suffered a whole lot due to the Dissolution.
No split with Rome and girls in Britain would be more educated overall, which could have more effects later, including the possible appearance of one or more Great (Wo)men who affect history in some way or another.