A row broke out after the British couple reportedly demanded an upgrade from economy to business class, and the pilot decided to offload the pair at a Portuguese air force base.
The incident occurred on flight BA2263 after it left Gatwick en route for Kingston on Wednesday.
The Daily Mail reports that the plane took off at around 11.35am and, by 3pm started to divert and turned back to the island of Terceira.
It then left the island at around 7.15pm, returning to London at 10.36pm.
According to the Telegraph, an air force spokesman told Agence France-Presse: "The pilot decided to land in Lajes in the island of Terceira because of a dispute between cabin crew and a couple who wanted to be transferred from economy class to first class.
"The British couple will remain in Terceira and will be questioned by police."
Meanwhile, another incident on Wednesday reportedly saw BA passengers left stranded on the runway for four hours without food.
The Standard reports that the flight was due to take off from London Heathrow for San Francisco at 11.30am on Wednesday but passengers were still on board the stationary plane by 3pm.
They were told there was a technical problem and disembarked at 3.30pm, before boarding a different aircraft at 6.25pm.
BA apologised for the delay and said a "technical fault with the aircraft resulted in an aircraft change". A spokesman added that passengers were later offered meal vouchers.