Constantine worked at the hospital during the Blitz. One night in January 1941, Jamie was brought to him as a patient. He tried some experimental therapy with the "empty" child in Room 802 and recorded it — his empathy likely due to losing his children and grandchildren to the war. Over time, every other person in the hospital was infected; first doctors and nurses, then patients. Constantine continued to care for them and keep them comfortable, but feared the Army would bomb the place and blame it on the Germans, as other cases were appearing all over London.
By the time the Doctor arrived, Constantine himself was the only one left unchanged by the plague, though he showed symptoms such as a scar on his hand. His presence seemed to keep the gas mask zombies subdued.
Constantine invited the Doctor to examine the patients around him. He explained how the symptoms spread. He tried to explain to the Doctor about Nancy's knowledge of events, but he succumbed to the plague himself and became a gas mask zombie like the others. He proceeded to threaten the Doctor, Rose Tyler and Captain Jack Harkness when Jamie found Nancy again. (TV: The Empty Child) The Doctor kept them at bay by sending them to their room.
He was among the victims of the plague summoned to the site of the Chula ship. When the nanogenes later recognised the correct human DNA, they repaired all those who had been infected, restoring Constantine, who was able to carry on his good work at the hospital. (TV: The Doctor Dances)
Constantine lost at least one child and at least one grandchild to the Blitz. He stated that he was "a father and a grandfather" before the war began and was now neither but was "still a doctor". The Doctor sympathasised with him, saying he "knew the feeling". (TV: The Empty Child)
Constantine was a dedicated doctor to the very end, keeping his patients comfortable despite their conditions. He was also selfless in death, ensuring the Doctor knew to find Nancy and knew the patients conditions despite nearing death from the nanogenes. (TV: The Empty Child)