The travellers said they were “left in the dark” while they were put up in a hotel, the Express reports.
Flight BA663 from Larnaca to Heathrow was due to leave at 7.30pm on Sunday night, before passengers were told they would not return until Tuesday.
The aircraft was delayed due to “technical difficulties”.
Families said they were struggling to contact travellers and received little information from the airline.
A spokesperson for British Airways confirmed there was a technical fault with the aircraft, the Express reported.
The spokesperson said: "We have apologised to our customers for the delay to their flight, and organised hotel accommodation for those who need it.
"The safety of our customers and crew is always our top priority, and cannot be compromised.”