Como eu digo "ação de perdas e danos" em inglês

Português: ação de perdas e danos, pedido de indenização, pedido de reparação por danos.
Inglês: action/ (law)suit/ claim for damages, claim for redress/ reparation/ compensation, request for compensation for damages.

Exemplo 1: Kay Springham KC and Dominic Scullion, Advocate recently appeared in the UK Supreme Court in a landmark action for damages brought by a lawyer against the Lord Advocate for assaults allegedly committed by a judicial office holder. Ref. compasschambers

Exemplo 2: The plaintiff organisation, which says it is a society registered under the Societies Registration Act, 1860 and also registered as a Public trust under the provisions of the Bombay Public Trust, 1950, has filed the suit for damages and also sought permission to file as an indigent person. Ref. m.economictimes

Exemplo 3: PwC is facing a lawsuit for damages of around £6.6m from Revelan. Ref. uk.finance.yahoo

Exemplo 4: (...) the High Court of England & Wales has agreed to hear a claim for damages brought by a claimant who is now an amputee following a road traffic collision in Portugal. Ref. stewartslaw

Exemplo 5: Bates, who revealed this weekend that he had been given a final “take it or leave it” offer that amounted to 49.2% of his original claim for redress, has said he believes that it is crucial to take future schemes out of government hands. Ref. theguardian

Exemplo 6: She explained how the people calling for reparations need to be in a "position of strength" and to be knowledgeable about all that transpired if they want to make a solid claim for reparation, but "more work needs to be done." Ref. cbc

Exemplo 7: If you have had a claim for compensation or reimbursement rejected by an airline they should clearly explain why it has been rejected. Ref. caa.co

Exemplo 8: (...)which arises other than under the ordinary contract payment provisions or a request for compensation for damages incurred by any party to a contract which was not anticipated in the terms of the original contract. Ref. qgs

OBS.: Nesse contexto, podemos encontrar a estrutura lawsuit seeking damages, que significa uma ação que busca por indenização.

Exemplo 9: Tesco, the largest retailer in the United Kingdom, has filed an antitrust lawsuit seeking damages from several salmon suppliers. Ref. intrafish