“Restrictions of this sort are only ever applied to maintain safety,” Nats said, adding staff were working “closely with the airports and airlines to minimise disruption”.
Passengers should check the status of their flight with their airline and airport, Nats added.
Data from flight tracking website Flightradar24 showed dozens of outbound flights were cancelled from Manchester, Gatwick and Heathrow airports, while hundreds more were delayed.
Inbound flights were also cancelled or delayed, Flightradar24 data showed.
Irem, 36, had her flight from Germany to the UK delayed by nearly seven hours due to fog at Manchester Airport.
“We’ve started boarding [at Cologne airport] but are crammed into a space where we’re waiting for the bus. We’ve been standing for about an hour, it’s just been a bit of a nightmare,” she told the BBC.
“I am from Cologne so we spent few days here over Christmas with my family. We are about to have a delayed Christmas and New Year with my husband’s family in North Wales.
“That will be delayed slightly, but I suppose we’re lucky we’re still going to see them tomorrow.”