The midwinter misery facing travellers is showing no signs of letting up, with road and rail journeys disrupted and delays and cancellations continuing at the UK's biggest airport.

As passengers struggled to get a flight at Heathrow, Transport Secretary Philip Hammond promised an inquiry into how services had virtually ground to a halt at the west London airport.

Commuters contended with a bitterly cold morning and many domestic rail services were disrupted, with some services cancelled, particularly in Scotland, and others delayed.

There were long queues for Eurostar Channel Tunnel trains at St Pancras station in London, while a number of accidents led to delays on some key road routes.

Some flights have been possible in and out of Heathrow, and Mr Hammond said that night-flight restrictions would be lifted at the airport for the next four days.

But as Heathrow passengers complained about being treated like "complete idiots", Mr Hammond said the airport was likely to be operating at reduced capacity over the next few days.

Heathrow operator BAA admitted there had been problems and the company was "extremely sorry for those".

London mayor Boris Johnson was among those critical of the situation at Heathrow, while shadow transport secretary Maria Eagle said she would have expected Mr Hammond to lead "a much better, more co-ordinated response" to the bad weather.

Mr Hammond said the railways were "broadly operating" and main roads were open and usable, and David Cameron's spokesman said the Prime Minister thought Mr Hammond had handled the disruption to transport effectively.

East Coast Main Line rail services were among those affected by the bad weather, while in southern England there were delays and cancellations for commuters coming into London from South-West England, from Bedfordshire and from East Anglia.