OThere will only be one SA Airways flight leaving from South Africa to London-Heathrow on Monday night, the airline said.
There would however be three flights coming into South Africa from London, said SAA spokesperson Fani Zulu.
He said Flights SA235 and SA237 from Heathrow would proceed as normal to their destination of OR Tambo airport in Johannesburg; as would flight SA221 from London to Cape Town.
However only SA234 would leave South Africa to London. The other two flights SA236, from OR Tambo and SA220 from Cape Town had been cancelled.
This is due to the authorities in London: "Whilst they are proceeding with operations in the airport there are restrictions with the flights coming into London, Heathrow.
"Several other airlines will be affected in the same way."
On December 18, Heathrow informed travellers that snow and adverse weather conditions had resulted in many cancelled flights and a build-up of delays.
BAA, the authority that manages the UK's main airports, said on Monday that Heathrow airport would be open and operating a limited schedule of arrivals and departures, but expected further cancellations and delays in the coming days.
This was as airlines had to move diverted aircraft and crew back to their normal positions and manage the impact of the poor weather over the weekend and in the days ahead, according to a statement posted on its website.
Other airports, such as Stansted, advised travellers to check with them first before going to the airport as "some flights may still be subject to delay or cancellation".
In France, about 40% of the flights at Paris's Charles-de-Gaulle airport were cancelled on Sunday.
Agence France Presse reported that French authorities had cancelled three out of 10 flights on Monday.
Frustrated SMS's and tweets from travellers opting to swop South Africa's wet Christmas for a white Christmas read along the lines of: "Flight got cancelled by snow storm". Many airlines inform customers by SMS of delays, but according to reports, some stranded travellers had bedded down in airport waiting halls.
Comment was not immediately available from the Airports Company of SA.
The Star reported that the greatest frustration was a lack of communication to travellers already at the airport.
Meanwhile, the UK's Daily Mail grumpily headlined their article on the subject: "Not our finest hour! Planes grounded, thousands of festive holidays ruined, roads ungritted, drivers stranded for hours . . . and all because it snowed".