Broad, 26, who has sat out the ongoing tour of India with a heel injury, was due to join his teammates ahead of next month's tour of New Zealand.
However, he revealed on Twitter his struggle to leave the ground.
"Been boarded. Now cancelled!!! 2nd time this week!!! Not been my week in airports! Oh well, could be worse right!!" the Nottinghamshire bowler wrote.
He then added: "Actually. It couldn't be much worse. Hotels at Heathrow bound to be full, freezing cold, I'm dressed for India, 7% phone battery. #cheers
"It's got worse! Airport too full to fit anymore passengers in! So stuck on plane til room is made! #itcouldbeworse"
Broad is the captain of England's Twenty20 side.