British Airways said fog was disrupting flights at Heathrow, Gatwick and City airports, while Stansted airport said it was experiencing "slight delays".
Those travelling were advised to check with their airline for updates.
Air travellers also faced delays on Sunday as foggy conditions caused problems.
A Met Office spokesman said: "Any fog will be slow to lift through this morning.
"Some brightness will develop by midday though and we should see sunny spells through this afternoon.
"Under any clear spells we could see fog patches tonight. Towards dawn low cloud will arrive from the north, bringing the risk of hill fog and drizzle too."
