As a brief note in advance: witch trials in Europe did not begin until the 15th century, and not in earnest until the 16th! You can find various parts of the witch stereotype well in action before then, but they are used to identify and condemn heretics, not Satan-worshipping, magic-practicing witches.

That said:

For England, the abolition of witchcraft as a political topic has a surprisingly straightforward answer: 1735, the passage of the Witchcraft Act [of 1735].

The law un-outlawed witchcraft, essentially...but it turned faking witchcraft into a crime. It was illegal to accuse other people of performing witchcraft; it was also illegal to turn a profit by claiming to be able to work magic yourself.

ETA: Oops, I missed part of the question, sorry!

I said "Witchcraft Act [of 1735]" because there were in fact numerous Witchcraft Acts before that. The central English government was absolutely keen on condemning witchcraft.

However, when it came to actually hunting, identifying, and punishing witches, the burden was on the local community. Malcolm Gaskill notes that witchcraft charges followed the common legal procedure in which charges were brought by the lay/civilian accuser, or accusers, and to a local court.

In Germany in particular, there are some infamous mass persecutions powered by an outside inquistitor on a full-scale torture spree of everyone in a town they could get someone else to name. But as horrific as that sounds, and how easily it fits with our nightmares of inquisitors, it was just not that common.