The Swedish website hosts links to download mostly pirated free music and video.
Sky, Everything Everywhere, TalkTalk, O2 and Virgin Media must all prevent their users from accessing the site.
“Sites like The Pirate Bay destroy jobs in the UK and undermine investment in new British artists,” the British Phonographic Industry (BPI) said.
A sixth ISP, BT, requested “a few more weeks” to consider their position on blocking the site.
BPI’s chief executive Geoff Taylor said: “The High Court has confirmed that The Pirate Bay infringes copyright on a massive scale.
“Its operators line their pockets by commercially exploiting music and other creative works without paying a penny to the people who created them.
“This is wrong - musicians, sound engineers and video editors deserve to be paid for their work just like everyone else.”