Heathrow airport's boss is to forgo a bonus, as snow-hit air and rail firms begin clearing their passenger backlog.
Colin Matthews said he was focussed on getting people moving and rebuilding confidence in the airport, which was criticised for its snow response.
Eurostar is operating almost normally but most national rail routes report problems, including East Coast again. Most airports warn of some disruption.
However, the Met Office has lifted all severe weather warnings across the UK.
Both runways at Heathrow are open and two-thirds of flights are operating. But travellers were warned not to expect services to return to normal straight away, and to travel to the airport only if their departure was confirmed.
In other developments:
- Delays and cancellations are reported on train services across the UK, although Network Rail says 70% are on time. National Rail Enquiries has more information
- Among the routes affected are most operated by Arriva Trains Wales and Scotrail, Virgin Trains services between London and both Manchester and Birmingham, and all First Great Western routes
- Signalling problems between Darlington and York meant delays and cancellations on East Coast mainline services
- Yorkshire Water has taken almost 7,000 calls from people reporting frozen pipes - nearly double the normal level
- Temperatures plummeted to -20.1C in parts of northern Scotland overnight
The Met Office predicts another cold day across the UK on Thursday, feeling particularly bitter across southern parts and with further snow showers likely in northern and eastern areas.
Meanwhile, NHS Warwickshire is appealing for drivers of 4x4 vehicles to spare a few hours over the next week-and-a-half to drive nurses to patients in snow-hit areas.
Director of communications Martin Turner said: "We've got a lot of patients in their homes and communities. Normally we would visit them week-by-week but a lot of regular cars can't get anywhere."
Some councils are concerned over supplies of road grit. With just 12,000 tonnes left in reserve across Wales, councils want Welsh ministers to ask the UK government to release some of the quantity stockpiled for English authorities.
Nottinghamshire, Wiltshire and Somerset councils have also asked for extra supplies.
Heathrow was criticised over the length of time it took to clear tonnes of snow following a blizzard on Saturday that dumped 5in (13cm) in just one hour.
Mr Matthews said: "We've had unacceptable conditions for passengers in the last few days. I'm responsible and I've decided not to take my bonus for 2010."
BAA would not say what its chief executive's reported six-figure bonus would have amounted to, but last year he received £994,000 in pay and bonuses, excluding shares.
Meanwhile, Heathrow said claims the airport had run out of de-icer, failed to order enough or accepted supplies from the government were "categorically untrue", after BMI airline chief executive Wolfgang Prock-Schauerit suggested it did not have enough of the fluid.
Prime Minister David Cameron had said weather disruption was understandable but he was "frustrated" at how long it took to improve the situation, while former Labour Transport Secretary Lord Adonis said BAA appeared to have made "totally inadequate preparations".
Mick Rix, the GMB union's national officer for the aviation industry who had called for Mr Matthews to give up his bonus, said: "For once, a British senior director has done the right thing."
British Airways says it has cancelled 2,000 flights and diverted 40 fully-laden planes to other airports around the UK and Europe over the past six days, one of its busiest periods of the year.
It hopes to operate a full long-haul departure schedule from Heathrow on Thursday and Christmas Eve and is using larger planes than usual on short-haul routes to accommodate more passengers.
Cross-Channel operator Eurostar said it planned to run 43 out of 52 services from London St Pancras on Wednesday, having restored normal check-in procedures.
It advised passengers to turn up only if they had a valid ticket, and only an hour before they travelled.
On Wednesday morning, some passengers were reporting empty seats on Eurostar trains out of London, despite people being left on platforms amid continuing chaotic scenes and long queues.
Asked about the country's travel problems, the prime minister said: "I completely understand and share people's frustrations when you can't get home, can't get to work, can't see loved ones and Christmas travel plans are sent awry."
But Mr Cameron insisted the government was "on top of the situation", having relaxed rules on night flights at airports and allowed lorry drivers to work longer hours.
The country had enough road salt and a good stock in reserve, he said, but added that priority had to be given to the strategic road network or motorways, A-roads and dual carriageways over treacherous side roads and pavements.
After suspending services because of damage to overhead power lines on Tuesday, Elaine Holt, the chairwoman of train operator East Coast, said: "Network Rail are going to look very closely at their infrastructure and what they can learn from this."
Rail watchdog Passenger Focus said the recent bout of cold weather should act as a wake-up call for the industry to provide better information.
Chief executive Anthony Smith said: "What we've seen recently is lots of cases where we've had websites saying different things, we've had phone lines saying different things and we've had staff saying different things as well."