Stranded passengers at Heathrow airport have been warned not to expect normal service to resume immediately after the airport's second runway reopened on Tuesday afternoon.

Thousands of people have endured uncomfortable nights in the airport's terminals as their travel plans suffer continued disruption due to the snowy weather, but BAA chief executive Colin Matthews warned people not to expect the situation to return to normal immediately just because the second runway has reopened.

"It is good news to see aircraft taking off and landing from two runways but it's really important that passengers understand that doesn't mean the full schedule is going to be restored instantly," he told Sky News.

"It's not just two runways we need - we need every other link in the chain to be fully up to speed and it's going to take some time to do that."

The airport plans to run about two-thirds of the schedule on Wednesday but it is "absolutely vital" passengers check first before going to Heathrow.

"It would be wrong for passengers to think that we are going to be back to full schedule tomorrow, because we are not," Mr Matthews added.

Meanwhile, Prime Minister David Cameron has spoken of his "frustration" at the length of the disruption at Heathrow.

Speaking at a Downing Street news conference, Mr Cameron said: "If it's understandable that Heathrow had to close briefly, I'm frustrated on behalf of all those affected that it's taking so long for the situation to improve.

"There have been intensive discussions between (Transport Secretary) Philip Hammond and BAA about how best to ensure that normal flying capacity is resumed as soon as possible."

There were also flight disruptions at Aberdeen, Edinburgh and Glasgow, as well as Gatwick, London Luton and London City airports, while rail travellers have also been affected by the freezing conditions, with hundreds of people having to be evacuated from stricken trains.

The East Coast line, one of the country's main railway arteries, was suspended between London and Peterborough, although it has reopened with a limited service operating. About 200 people were forced to climb down on to the tracks when an East Coast service came to a halt, and about 80 more passengers from two First Capital Connect services also abandoned carriages.