The volcanic eruption in Iceland on Wednesday night sent plumes of ash thousands of feet into the air. The cloud has spread across the UK to Europe.
Others switched from plane to train, with the East Coast line extending its 1830 BST London to Newcastle service through to Edinburgh.
A spokeswoman for Eurostar estimated an extra 10,000 seats had been booked.
She also said Friday's services were "extremely full".
Budget airline Ryanair said no flights were operating to or from the UK on Thursday and it expected cancellations and delays on Friday.
A spokesman for Nats, which was formerly known as the National Air Traffic Services, said: "The Volcanic Ash Advisory Centre has issued a forecast that the ash cloud from the volcanic eruption in Iceland will track over Europe tonight.
"Nats is working with Eurocontrol and our colleagues in Europe's other air navigation service providers to take the appropriate action to ensure safety in accordance with international aviation policy."
The European air safety body, Eurocontrol, said the cloud of ash had reached 55,000ft and was expected to move through northern UK and Scotland.
Brian Flynn, assistant head of operations of its central flow management unit, told the BBC: "As it moves toward the Netherlands and Belgium it will dissipate and lose intensity, like any weather phenomenon. But we don't know what the extent of it will be."
The Natural Environment Research Council (NERC) has sent up a reconnaissance flight to investigate how the ash is distributed in the cloud, something that is impossible to assess from satellite imagery.
Dr Mike Branney, senior lecturer in volcanology, University of Leicester, said: "Volcanic ash is not good to plane engines.
"Firstly it is highly abrasive and can scour and damage moving parts. Secondly, if it enters a jet engine the intense heat of the engine can fuse it to the interior of the engine with a caking of hot glass, which ultimately can cause the engine to cut out completely.
"This is a sensible precaution."
In 1982 a British Airways jumbo had all four of its engines shut down as it flew through a plume of volcanic ash.
There was also an incident on 15 December 1989 when KLM Flight 867, a B747-400 from Amsterdam to Anchorage, Alaska, flew into the plume of the erupting Mount Redoubt, causing all four engines to fail.
Once the flight cleared the ash cloud, the crew was able to restart each engine and then make a safe landing at Anchorage, but the aircraft was substantially damaged.
A BAA spokesman said: "Passengers intending to fly today are asked to contact their airline for further information."
The eruption under a glacier in the Eyjafjallajoekull area of Iceland is the second in the country in less than a month.
Prof Bill McGuire, professor at the Aon Benfield UCL Hazard Research Centre, said it was not "particularly unusual" for ash from Icelandic eruptions to reach the UK.
"Such a large eruption... would have the potential to severely affect air travel at high northern latitudes for six months or more.
"In relation to the current eruption, it is worth noting that the last eruption of Eyjafjallajoekull lasted more than 12 months."
