Law firm Leigh Day filed a lawsuit against UEFA and UEFA Events on Monday, according to publicly-available records of cases brought at the High Court.
The firm told Reuters it has issued claims on behalf of 887 individuals and has a total of 1,076 clients.
Two other law firms, Pogust Goodhead and Liverpool-based Binghams Solicitors, said last year that they also represent Liverpool fans who intend to sue UEFA.
UEFA did not immediately respond to a request for comment on the legal case.
Its general secretary Theodore Theodoridis said last month, when UEFA announced it will refund Liverpool fans who had certain tickets, that "we recognise the negative experiences of those supporters on the day".
The governing body has apologised after initially blaming Liverpool fans for the mayhem, which delayed last year's final by 36 minutes after thousands of Liverpool supporters were unable to get into the Stade de France for the match against Real Madrid on May 28.
French police were filmed using tear gas on fans, who complained of heavy-handed treatment as they were herded into pens outside the stadium.
An independent review of incidents outside the stadium, released in February, found that UEFA was responsible for a "large number of near misses that nearly led to disaster" before the final, which Real Madrid won 1-0.
