It comes as most flights to and from Northern Ireland were cancelled for a fifth day because of the threat posed.
Thousands of passengers remain stranded with planes grounded across Europe.
Air traffic control body Nats has extended restrictions in UK airspace until 0100 BST on Tuesday. Irish airspace is closed until 1800 BST.
The airlines are becoming increasingly critical of the way the authorities have responded since ash from a volcano in Iceland contaminated the atmosphere five days ago.
The airlines have said the total flight ban is misguided and is devastating their industry.
EU Transport Commissioner Siim Kallas said: "We cannot just wait until this ash cloud dissipates."
On Monday Gordon Brown announced that the Royal Navy will help repatriate UK travellers who have been stranded overseas as UK airspace remains restricted.
Three Royal Navy ships, HMS Ark Royal, HMS Ocean and HMS Albion are heading for Spain and unspecified Channel ports.
The move was announced after the UK's emergency committee Cobra met to discuss options in addressing travel chaos caused by a volcanic ash cloud.
More than 6.8m passengers have been affected so far and 63,000 flights have been cancelled since Thursday.
According to the Association of British Travel Agents, about 150,000 people are still stranded.
Senior EU officials have expressed hope that up to half of all flights will be able to operate today.
Airports and airlines have questioned the need for curbs said to be costing airlines alone $200m (£130m) a day.
Two groups representing European airport operators and airlines have demanded "an immediate reassessment of flight restrictions".
British Airways is among several airlines which have now carried out test flights without incident.
However, a Met Office plane did encounter dangerous levels of ash.
Nats said Met Office forecasts showed the ash cloud progressively covering the whole of the UK.
"Anyone hoping to travel should contact their airline before travelling to the airport," it added.
The Irish Aviation Authority said: "Met experts are predicting that the prevailing weather conditions will continue in the coming days. Ongoing restrictions are therefore likely."
Airspace remains closed, or partially closed, in more than 20 countries.
Belfast International Airport spokesman Uel Hoey said: "We are at the end of a long line and the authorities and experts need to decide when it is safe to fly."
He said a few people had turned up at the airport, hopeful that they might get their flights.
The atmosphere was "surreal", he said.
"The ironic thing is that since Thursday the airport has remained open to facilitate flights but obviously those flights depend on having safe and conducive conditions for the aircraft to operate so we are very much at the end of the chain".
Katie Best of Belfast City Airport said staff were on hand to deal with enquiries and help people make alternative arrangements.
"We have staff on the gates at the airport here so people are given an update and told that nothing is flying and that they can make their onward journey from there as appropriate," she said.
Flybe has cancelled all flights due to operate on Monday and it has asked passengers not to go to George Best Belfast City Airport.
Aer Lingus said its UK, European and US flights scheduled to depart on Monday have been cancelled. This includes Aer Lingus regional flights.
Ryanair has cancelled all scheduled flights to and from the UK and Ireland until 1300 BST on Wednesday.
Prof Brian Golding, head of forecasting research at the Met Office said it was likely the volcanic cloud would remain over the UK for several days.
"We need a change of wind direction that stays changed for several days and there is no sign of that in the immediate future," he added.
Experts say the tiny particles of rock, glass and sand contained in the ash cloud could jam aircraft engines, as has happened in previous incidents of planes flying into plumes of volcanic ash.
The last eruption of the Eyjafjallajoekull volcano system that is creating the problems was on 20 March, when a 0.5km-long fissure opened up on the eastern side of the glacier at the Fimmvoerduhals Pass.