"Video Nasty" was a colloquial term coined in the UK in the early 80's to describe movies believed to contain extreme sexual violence and gore (but often didn't). The Director of Public Prosecutions (DPP) drew up a list which was made public in June 1983 of 72 films.
39 of these were successfully prosecuted under the Obscene Publications Act. Among the many people prosecuted was David Hamilton Grant of World of Video 2000 who was sentenced to 18 months in jail in February 1984. In September 1985 The Video Recordings Act (VRA) was signed into law prohibiting the supply of uncensored/unclassified videos. This is that list (including the 'Video Nasties' and 'Ban The Sadist Videos' documentaries).
Other 'Nasties' that didn't make the DPP list are listed here: Video Nasty by Association