Christopher Bainbridge, 45, from Darlington, was found dead in a wooden camping pod at the Quiet Site Caravan Park in Watermillock, Penrith.
His wife Jane, 42, was taken to Cumberland Infirmary where she remains in a serious condition.
Ambulance staff said early indications suggested they had been poisoned by carbon monoxide.
Site owner Daniel Holder said: “At this time we are helping the police fully with their inquiries and obviously our condolences go out to the family of those concerned.”
Cumbria Police said an investigation into the cause of the accident has begun.
A post-mortem examination is being held on Thursday and a file is being prepared for the coroner.