Heathrow has told passengers due to fly from Terminal 1 and Terminal 3 not to go to the airport, as there is not enough space for them.
Airport operator BAA said this afternoon that both terminals were "extremely congested" and added: "We are unable to accept any more passengers coming to these terminals."
Passengers who have arrived but are unable to travel are being offered free travel back to Paddington Station on the Heathrow Express.
The airport remains open and is operating a limited flight schedule. Passengers are being warned to expect further cancellations and delays for at least the next few days, as airlines move diverted aircraft and crew back to their normal positions.
Most other airports in the UK are warning of delays and cancellations, not only due to operational difficulties but also due to the knock-on effects of snow at other airports meaning aircraft are unable to reach their destination.
Belfast, Manchester, Aberdeen, Edinburgh and Glasgow, Southampton airports are open, but flights are operating with delays and cancellations. London City airport is also open, but a number of flights were cancelled earlier this morning, and others are experiencing delays.
Gatwick's runway is open and operations are returning to normal, but as with other airports, passengers should check with their airline to confirm the status of their flight.
Frankfurt, Paris Charles de Gaulle and Paris Orly airports have also been affected by the severe weather – all three had to cancel flights this morning, and warned of further delays today.