Airport authorities said the weather had forced the cancellation and advised passengers to check their flight status before heading to the airport.
"We've had to cancel flights to keep up with the schedule. Passengers are advised to check with their airlines," said a Heathrow spokesperson.
Meanwhile, an Air India flight from Delhi, which had to be diverted to Paris, was able to land in the UK a few hours later.
The disruption at Heathrow comes on the last day of the school half-term holidays for much of the UK and families would be heading back home this weekend.
More From This Section
"The thick fog is expected to return again tonight so Heathrow could be pretty foggy again tomorrow morning."
The Met Office has issued a yellow weather warning for most of England and parts of Wales tonight, and drivers are being urged to slow down because of reduced visibility.
Dense fog is expected to remain tomorrow morning, causing traffic delays as pupils return to school after the week-long holiday.
The Gunpowder Plot conspirators were bent on assassinating Protestant King James I for his refusal to grant greater religious tolerance to Catholics and planned to blow up the Palace of Westminster during the state opening of Parliament.