Another day of cancelled trains, but it's going to be 50 degrees next week

A number of train companies ran amended timetables, with some services axed on the main London to Scotland routes up the east and west coast.

East Coast axed eight London-Leeds trains and ran amended services on some other routes.

The RMT transport union said it was "scandalous" that train companies could bring in "special" timetables and avoid financial penalties.

As travellers endured yet another bitterly cold day, forecasters said that should the icy weather continue, the UK could be heading for its coldest December since 1890.

But they added that temperatures could rise as high as 10C (50F) by the middle of next week as a new weather system moves in from the Atlantic.

First Capital Connect, Chiltern and Merseyrail were among passenger train companies running amended services today.

Chiltern was not only operating reduced services but also running shorter trains on some routes.

ScotRail axed a number of services, including Glasgow Queen Street to Anniesland via Maryhill, Glasgow Queen Street to Cumbernauld, Dalmuir to Springburn, Edinburgh to Perth, Newcraighall to Cowdenbeath and Glasgow Central to Ardrossan Harbour.

West Coast main line operator Virgin Trains said some services were subject to delays of up to 60 minutes, with trains to and from Glasgow Central and Manchester Piccadilly the ones most affected.

National Express East Anglia and Stansted Express services were running to a reduced timetable, as were the services operated by the Northern Rail train company which had to axe its York to Sheffield via Pontefract services.

London Midland had service alterations today, with trains between London and Tring in Hertfordshire not running.

Bob Crow, leader of the RMT transport union, said: "It's a scandal that the private train operating companies can simply chop 25% of their services, install a 'special' timetable and avoid financial penalty.

"This racket shows that the private rail franchise system is rigged in favour of the train operators and means that they can provide what services they like, when they like, leaving passengers out in the cold while the train companies are laughing all the way to the bank.

"These rail companies have ripped off 2 billion from the network since privatisation in profits and subsidies and the time has come to kick these spivs and chancers off the tracks and return the railways to public ownership."

British Airways was operating all its long-haul flights at Heathrow airport as well as the vast majority of short-haul services.

Where possible, BA flew larger long-haul aircraft to European cities today to increase its seat capacity. The airline was also hiring extra aircraft to help fly as many passengers as possible.

BA added: "In an attempt to free up even more seats, we are continuing to encourage customers who hold bookings to or from Heathrow up until the end of New Year's Eve to either rebook for a later date or claim a full refund if their journey is not essential."

Away from Heathrow, other UK airports had to cancel some short-haul flights due to the continuing bad weather in Europe.

At Birmingham airport, flights to and from Brussels and Paris were affected, while Aberdeen and Edinburgh airports warned passengers to expect delays and cancellations.

Most main roads in England remained clear this morning, but the Highways Agency warned drivers to expect widespread frost tonight, with the temperature likely to fall below minus 10C in central and western areas.

Forecasters said that parts of Scotland and possibly north east England were the only places likely to have snow falling on Christmas Day.

"This is certainly the coldest December since 1981 but where it stands in the all-time cold Decembers rather depends on what happens in the next few days," said Steven Davenport, a senior forecaster at MeteoGroup, the weather division of the Press Association.

He went on: "This December has the potential to be the coldest since 1890 when the central England temperature (an average for the month) was as low as minus 0.8C (30F).

"But a system is moving in from the Atlantic that will bring less cold air. This could lead to heavy and prolonged snow on the night of Boxing Day and into next Monday but after that temperatures in south-west England, and possibly London, could be as high as 10C (50F) by Wednesday."