The main witch persecutions that resulted in actual deaths started in the 16th century, mainly due to economic and social pressures resulting from the Reformation. (See Religion and the Decline of Magic by Keith Thomas). People had previously relied on the charity provided by the monasteries; once these were dissolved in England, there were a lot more poor old people around asking for handouts. People felt guilty for not helping them, so when the old women went away mumbling, they assumed that they had been bewitched when they got psychosomatic symptoms resulting from their feelings of guilt. Also the Catholic Church had provided oodles of protection against sorcery, in the form of holy water, amulets etc., whereas the Protestants just told people to pray. Great.
The Inquisition was more interested in persecuting heretics, especially conversos (Jews and Muslims forcibly converted to Catholicism) in Spain. The majority of people judicially killed for witchcraft were in Protestant areas.
The witch persecutions in England differed in character from those in the rest of Europe. The things people were accused of were different. In Europe, witches were accused of flying to Sabbats and having intercourse with the devil; frequently, midwives were accused of performing abortions and stealing children (source: numerous broadsheets in German). In England, they were accused of having witches' teats to give suck to their familiars; bewitching cattle etc. In Europe and Scotland, witchcraft was a heresy, and therefore subject to ecclesiastical law, with the penalty of being burnt. In England, witchcraft was a felony, subject to criminal law, and the penalty was hanging.
There is no unbroken line of witch religion stretching back into the mists of time. The foundation date of modern Wicca appears to have been sometime in the 1920s, according to the latest research by Philip Heselton in Gerald Gardner and the Cauldron of Inspiration (an excellent book, as was its predecessor, Wiccan Roots). During the nineteenth century (and possibly the eighteenth century), there were various people who either self-identified as cunning folk or witches, or were labelled as such by their neighbours. However there was no organised movement of witchcraft, only isolated groups 'reinventing the wheel' - and they weren't necessarily pagan either - much of their magic was based on Christian symbolism (cf the story Marklake Witches by Rudyard Kipling). Note that the cunning folk were not witches - during the period of persecution they had often accused women of being witches and handed them over to the authorities.
In England, small snippets of Pagan belief and practice had survived and been incorporated into folk belief and practice - but again there was no large-scale survival of ancient Paganism. In some of the more remote corners of Europe (e.g. Scandinavia and Lithuania), ancient Paganisms survived much longer, and so when they were revived, the revivals were much closer to the original forms. There were also traditional practitioners of magic in Finland, particularly among the Sami people.
People really should be forced to read Triumph of the Moon: a history of modern pagan witchcraft by Ronald Hutton before they are allowed to make pronouncements about the history of witchcraft.
There's also an excellent article by Jenny Gibbons, Recent developments in the study of the Great European Witch Hunt, originally published in The Pomegranate, the journal of Pagan Studies.