The family-of-four from south Wales successfully sued Cook after suffering vomiting and diarrhoea while staying at the Steigenberger Aqua Magic Hotel in April 2016.
Last month (July), Cook was ordered to pay out £26,000 compensation and costs after the family brought a case with JMW Solicitors.
The case, said JMW, centred around temperature logs and cleaning records which purported to have been signed off by four different people but were found to have been completed by the same person.
John and Susan Cooper fell fatally ill at the hotel last Tuesday (August 21) while holidaying with Cook.
An investigation into their deaths is under way, with forensic teams assessing the food, water and air conditioning at the hotel.
They have collectively promised a full, thorough and transparent investigation into hygiene standards at the hotel.
The Egyptian authorities have said the couple died of natural causes. Cook has said there is no evidence to suggest the couple died of carbon monoxide poisoning.
Cook pulled all 300 of its guests out of the hotel, offering them alternative accommodation or flights home.
Fankhauser has confirmed 13 guests at the hotel are understood to have been suffering food poisoning when Mr and Mrs Cooper, a Thomas Cook agent in Burnley, died.
However, JMW Solicitors have said they believe at least 40 people have been struck down over the past week at the Steigenberger Aqua Magic resort.
Speaking to BBC Wales, partner Joanne Brine said the family accused Cook of failing to ensure food was “safe for human consumption” and permitting food to be “re-served or re-used on more than one occasion”.
She added that as the family had been on an all-inclusive Cook holiday, they had only eaten and drunk at the hotel restaurant.
Cook has said the hotel was last audited in July 2018, scoring 96%.
In a statement issued by JMW, Brine added the deaths were “incredibly concerning” in light of her clients experience more than two years earlier.
“The fact we have brought concerns to Thomas Cook’s attention about the accuracy and reliability of the hotel’s record keeping should set off alarm bells for those investigating.
“I sincerely hope a thorough investigation will make sure the [Cooper] family get the answers they need to understand exactly what happened inside that hotel room and ensure the safety of future holiday makers is prioritised.”
A Thomas Cook spokesperson said: “The safety and wellbeing of our customers is always our first priority and we would never send customers to a hotel which we do not believe to be safe.
"We audit all 3,000 of our core hotels every year and so far this calendar year we have removed 47 hotels for health and safety reasons and a further 150 which did not meet our strict quality criteria.
"As well as the audits, our quality teams regularly inspect our properties and provide support, guidance and training to help hotels improve.
"We last audited Steigenberger Aqua Magic in July 2018.”