According to The Sun, the teenage actors began romancing after growing close on set.
Scodelario (Effy), 17, and O'Connell (Cook), 18, shared romantic scenes in the E4 drama, on which their characters are involved in a love triangle with Freddie, played by Luke Pasqualino.
"They are a really sweet couple," said a source. "It took a while for them to get together but while filming such risqué scenes they grew close.
"They are trying to persuade scriptwriters to get their characters back together."