Airlines have begun to question the level of restrictions to UK flights.
David Henderson, of the Association of European Airlines, told the BBC the lockdown on flights was an overreaction.
He said: "We believe that flying should be taking place."
Across Europe some 14,000 flights are expected to take off on Tuesday - about half the normal number - and planes are being permitted to fly over the UK at altitudes above 20,000 ft.
But Transport Secretary Lord Adonis said the safety of air passengers remained the "paramount concern".
The minister, who said he had maintained a constant dialogue with European and UK regulators regarding flights, added: "All decisions being taken by the aviation regulators are intended solely to protect the travelling public, and I will not compromise passenger safety."
Meanwhile, British Airways has said 12 long-haul flights were currently en route to Heathrow, from Beijing, Singapore and the US west coast.
A spokeswoman said the airline had contingency plans for each flight if Heathrow was still closed but would not say which airports it would use instead.
It had been hoped that the intensity of volcanic eruptions was reducing, but the emergence of a new ash cloud has meant plans to reopen British airspace have been revised.
Jonathan Astill of Nats said the new ash cloud was a "significant change" to the situation on Monday.
He told BBC News: "The Met Office is reporting a further ash cloud that is coming down from Iceland and then covering the UK progressively during the day."
In a statement, Nats said: "The situation regarding the volcanic eruption in Iceland remains dynamic and the latest information from the Met Office shows that the situation will continue to be variable."
Schedules are constantly changing and passengers have been advised not to travel to airports until they have checked with their airline or tour operator.
The first international flight from Glasgow was due to head for Reykjavik in Iceland at midday.
TUESDAY'S AIRLINE DISRUPTION
- no short-haul services on Tuesday, but 12 long-haul flights
- flights to/from northern Europe, including UK, cancelled until 0100 BST on Wednesday.
- flights cancelled to/from the UK, Ireland, and much of northern Europe until 1300 BST on Wed 21
- flights scheduled between Aberdeen, Belfast City, Edinburgh, Glasgow, Inverness and Newcastle from 1005 BST
- plans to resume UK domestic flights from Heathrow at 1900BST and from regional UK airports from 1300 BST
- Certain internal and European flights operating, some cancellations on Tuesday and Wednesday
*All passengers are advised to check with their airline before heading to the airport
Nats said the latest Met Office information meant the part of Scottish airspace that had been open for much of Tuesday, including Aberdeen, Inverness and Edinburgh airports, would continue to be available to 0100 BST on Wednesday, and also south to Newcastle Airport.
Teesside airport will also be available between 1900 and 0100. Glasgow airport, which had been open on Tuesday morning but ran no flights after 1300 BST, will re-open for the same period.
No airports south of Newcastle, however, will be allowed to run flights before 0100.
The spread of volcanic ash has affected large swathes of Europe for the past five days.
There has been huge disruption for air travellers, many of whom have embarked on long and costly journeys over land and sea to get home.
Pilots' association Jim McAuslan: "Final decision rests with the pilot"
A small number of flights have taken off in northern Europe with planes departing from Paris, Amsterdam and Frankfurt - although many flights have been cancelled.
He said the government is maintaining increased capacity for passengers to cross the channel.
There are an extra 20,000 passenger places a day across Eurostar, Eurotunnel and the ferries, according to the minister.
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