Liverpool fans outside the Stade de France
A recent independent report found Uefa bore "primary responsibility" for what almost led to a "mass fatality catastrophe" in Paris last May.
Fans were penned in and sprayed with tear gas outside the Stade de France as kick-off was delayed by 36 minutes.
Law firm Leigh Day has issued Uefa with a group personal injury claim.
The Liverpool-based firm issued the claim on behalf of 887 clients at the Liverpool District Registry of the High Court on Monday.
Leigh Day is bringing the claim on the basis European football's governing body had failed to ensure a safe and secure environment for those attending and could owe a legal liability to those who suffered physical or psychological injuries.
In September, law firm Bingham's teamed up with global law company Pogust Goodhead in a lawsuit for 1,450 clients, suing Uefa for breach of contract in ticket sales and negligence over a duty of care they had towards supporters, who were harmed physically and psychologically.
Earlier this year, Uefa said it would refund Liverpool fans who had tickets for the final against Real Madrid.
The governing body and French authorities initially blamed ticketless fans for the events outside the stadium, but the independent report - which Uefa commissioned after the 28 May showpiece - said there was "no evidence" to support the "reprehensible" claims.
Uefa president Aleksander Ceferin appeared to allude to his organisation's failings at the final at Wednesday's Uefa Congress in Lisbon.
"We must never forget the mistakes of the past and we must remain humble at all times," he said.
"Unfortunately, unlike goalkeepers, leaders can never keep a 'clean sheet'. No leader can boast an unblemished record, however much they invest and however passionate, professional or experienced they are.
"There are always a few stains, a few mistakes that tarnish our reputation, errors they would love to erase.
"I am no different and Uefa is no different. The most important thing is to understand the mistake and change, not to repeat them."
-- Courtesy of BBC Sport