Richard Griffin, 64, William Hammersley, 79, and Harry Cadman, 71, died after contracting the disease in 2012.
An initial Health Protection Agency (HPA) report said the disease originated from a hot tub on display at the JTF Warehouse in Fenton, Stoke-on-Trent.
Griffin, from Clayton, Staffs, died on August 2, 2012, after spending a week in hospital.
Hammersley, from Chesterton, Staffs, died on August 4 while Cadman, from Stoke-on-Trent, died days later.
A further 18 people needed hospital treatment.
Thirteen cases were settled out-of-court, but families of those who lost relatives who contracted the disease are pursuing their cases through the courts.
Personal injury lawyers Irwin Mitchell have issued formal court proceedings against JTF Wholesale Limited, which has 13 branches across the UK. Jatinder Paul is running the case for Irwin Mitchell. He told HW JTF had admitted liability.
Inquests are to be held this year and JTF’s insurers have already admitted civil liability on behalf of the firm for causing the outbreak.
JTF said: "JTF takes its responsibility for the safety of all who work at and visit its stores extremely seriously and is saddened by the events which occurred in 2012. The company would wish to extend its sympathy to all those affected by the legionella outbreak and in particular its condolences to the families and friends of the three people who sadly died. Unfortunately, due to ongoing investigations by the police and the pending inquests into the deaths of those who died JTF is unable to make any further comment."