John Cooper, 69, and wife Susan, 63, died during a stay at the 394-room Steigenberger Aqua Magic hotel in the Red Sea resort on Thursday (August 23).
The operator said Mrs Cooper was a "loyal and long-serving" Cook employee at its Chancery Walk store in Burnley. It is understood the couple were were holidaying with their daughter and their grandchildren.
Carol MacKenzie, Cook’s head of customer welfare, flew out to Hurghada on Thursday to support the Cooper family.
In a statement, Cook said it would start evacuating guests from the hotel on Friday morning.
Acknowledging the circumstances of the Coopers’ deaths were still unclear, the operator said the move was a "precautionary measure" while it investigates "a raised level of illness".
Its 301 customers staying at the Steigenberger will be offered alternative accommodation or flights home.
A Foreign Office spokesperson said: "We are supporting the family of a British couple who died in Hurghada, Egypt, and we are in contact with the local tour operator."
