"As a result of the terrible incidents in Brussels, we have increased our security presence and patrols around the airport," the airport said in a statement.
Cameron earlier said on Twitter he was "shocked and concerned" by the events in Brussels.
"I will be chairing a COBRA meeting on the events in Brussels later this morning," Cameron said.
COBRA meetings are held to discuss how the government responds to emergency situations and bring together ministers, police and intelligence officers.