Passenger Sean Mallon told BBC Radio Ulster "about 95%" of seats were occupied, adding there was "no social distancing whatsoever" onboard.
Mallon said the airline did not offer any guidance on social distancing before the flight, with passengers allowed to queue and board as normal.
He also revealed no additional precautions were taken such as providing hand sanitiser, and the only advice given to passengers was for them to wash their hands after landing.
In a statement provided to the BBC, Aer Lingus said: "In light of the unexpectedly high loads on the Belfast-London Heathrow service this morning [Monday] and the level of demand for the route, Aer Lingus is reviewing its processes and procedures applicable to the operation of this service.
"The safety and security of Aer Lingus’ customers and crew is our top priority and any process changes that are identified as being required will be implemented as a matter of urgency."