The problem was to a computer glitch that affected the airport's Terminal 5, which handles British Airways flights, the British Broadcasting Corp. reported.
"There are now thousands of people with missed flights, as planes went on time," said passenger Simon Frusher, on his way from London to New York.
The BBC said there were about 500 travelers queued up to get on another flight.
The problems began about 9 a.m. and were resolved by 11:30 a.m., the BBC said.
"Our teams have now restored all check-in services and we have additional staff in the terminal to help passengers," an airport representative said.
The airport said passengers with carry-on luggage were not affected, but others were prevented from checking in and traveling.
A BA spokesman apologized for the inconvenience to those who missed their flights, while noting "all of our flights continue to operate as normal."