Air travel across Europe has been severely affected, with a raft of countries from Belgium to Switzerland completely closing their airspace, while others like Austria, Germany and Poland have enforced partial closures.
Despite the ongoing restrictions in England, Nats said airports in Manchester, Liverpool and all airports to the north of those may be available for some flights between 0400 BST and 1000 BST on Saturday.
This would be for some departures to and arrivals from the north and west.
But it added that forecasts indicated the ash cloud was expected to return over northern England at 1000 BST and it was likely that restrictions would be reintroduced.
Nats is due to make its next statement at 0900 BST.
Transport Secretary Lord Adonis warned passengers there was likely to be "significant disruption" for the next 48 hours.
European air traffic control organisation Eurocontrol said about 60% of flights within Europe had been grounded on Friday, representing about 17,000 services.
More than half of the normal 300 trans-Atlantic flights had also been cancelled.
Travel disruption: The picture around the UK
Spokesman Brian Flynn added: "Given the fact that this volcanic ash cloud has been quite stable and moving very slowly since it started 48 hours ago, it is reasonable to assume that there will be significant disruption of European air traffic tomorrow."
The Civil Air Navigation Services Organisation (Canso), a global association of air traffic control companies, said the knock-on effect would probably disrupt European airspace for several days.
"Traffic will have to be reorganised and rerouted and flights re-planned, all on a dynamic and quite unpredictable basis," it said in a statement.
In other developments:
British Airways cancelled all its flights to and from London airports on Friday and Saturday
said it would close its airspace from midnight (2200 GMT) and Romania is to close its airspace over the north-west from 0300 BST (0000 GMT) on Saturday
Ryanair cancelled all flights to and from northern Europe until 1300 BST on Monday. It will keep running in southern and central Europe, although flight restrictions are being imposed in Hungary and Romania
The Jet2.com airline cancelled all its flights on Friday and Saturday, adding additional flights for Sunday and Monday
P&O Ferries said it had dealt with 30,000 calls on Friday - the most it had dealt with on one day in its history. It said it would be unable to accept any further foot-passenger bookings
Network Rail said it had cancelled some planned weekend engineering work so more trains could run
Over the next 24 to 36 hours, prevailing winds will shift slightly to drive the central part of the ash plume further to the north toward Scandinavia, according to BBC weather forecaster Matt Taylor.
"However, later this weekend, [the winds] will return to a northwesterly direction and are more likely to bring the risk of ash back to the UK."
Although the winds can be predicted, the crucial factor is how much ash the still-erupting volcano is pumping into the atmosphere.
A reconnaissance flight to investigate how the ash is distributed in the cloud has now taken place, with the results due to be analysed later.
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 Health Protection Agency has stressed the ash does not pose a significant risk to public health, and Health Protection Scotland says only a low concentration of particles is expected to reach the ground.
It advises that some people with respiratory problems may experience short-term effects, but there should be no serious harm.
Stranded passengers have flooded other modes of travel. Eurostar trains reported a complete sell-out of its services to Brussels and Paris for the second day on Friday.
"We are carrying more than 38,000 people today and all our trains are full," a spokeswoman for the company said.
"We are telling potential customers without bookings not to come to St Pancras because they will not be able to travel."
The Ministry of Defence says 550 military personnel are grounded in Cyprus as a result of the travel restrictions.
Rail and ferry services are reporting rises in their passenger numbers, with ferry operators Stena and Fastnet saying there were significant increases in customers on services departing from Wales.
The last eruption of the Eyjafjallajokull 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.
The eruption prior to that started in 1821 and continued intermittently for more than a year.
Have you been affected by the volcanic ash cloud? Are you stranded because of the airspace restrictions? Are you in Iceland? You can send your experiences using the form below:
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