The MPA started legal action against the ISP last month in a bid to ensure BT did not allow web users to access Newzbin 2, a members-only site that offers links to other locations on the web where music, movies and other content can be illegally downloaded.
"In my judgment it follows that BT has actual knowledge of other persons using its service to infringe copyright: it knows that the users and operators of Newzbin2 infringe copyright on a large scale, and in particular infringe the copyrights of the Studios in large numbers of their films and television programmes," said Justice Arnold, who was preceding over the case.
"It knows that the users of Newzbin2 include BT subscribers, and it knows those users use its service to receive infringing copies of copyright works made available to them by Newzbin2."
Justice Arnold also ruled that BT must use its own Cleanfeed technology, which is already used to block access to websites containing child sex abuse images, to prevent access to Newzbin2.
The MPA initially started legal action against the original Newzbin in 2010, which resulted in the site being ordered to remove any material that infringed copyrights. However, Newzbin went into administration and was subsequently sold to new owners and launched again as Newzbin 2 from the Seychelles.
The ruling marks the first time an ISP has been ordered to block access to a website relating to illegal downloads.
"This ruling from Justice Arnold is a victory for millions of people working in the UK creative industries and demonstrates that the law of the land must apply online," said Chris Marcich, President and Managing Director (EMEA) of the MPA
"This court action was never an attack on ISPs but we do need their co-operation to deal with the Newzbin site which continually tries to evade the law and judicial sanction. Newzbin is a notorious pirate website which makes hundreds of thousands of copyrighted products available without permission and with no regard for the law."
The MPA also said it is likely it will now request other ISPs to block the site.
A BT spokesman said the judgement was "helpful" and "provides clarity on this complex issue".
"It clearly shows that rights holders need to prove their claims and convince a judge to make a court order. BT has consistently said that rights holders need to take this route. We will return to court after the summer to explain what kind of order we believe is appropriate."
Nicholas Lansman, Secretary General of the Internet Service Providers Association (ISPA) said blocking websites featuring illegal content is "an issue that rights holders should seek to address in court, rather than through voluntary means".
"Today's ruling should go some way to offering clarity on what is a complex area. However, concerns about over-blocking, ease of circumvention and increased encryption are widely-recognised which means that blocking is not a silver bullet to stop online copyright infringement," he said.
"Rather, as the government-commissioned Hargreaves Review recently found, there should be more focus on offering innovative, fully-licensed content services to give consumers what they are clearly demanding."