There had been hope airports in northern England would reopen
The ban on flights in English airspace has been extended until at least 1900 BST on Sunday because of the threat posed by a cloud of volcanic ash.
Flights were grounded on Thursday after the eruption in Iceland.
Flights between Cornwall and Scilly were halted on Saturday after ash was found on an aircraft. Ash was also reported falling across Devon.
Airport sources suggest officials are preparing for nationwide disruption to continue until at least Wednesday.
In a statement, Nats said: "The volcanic ash cloud from Iceland is moving around and changing shape.
"Based on the latest information from the Met Office, Nats advises the restrictions currently in place across UK-controlled airspace will remain in place until at least 1900 BST on Sunday.
"After 1900 BST, Met Office forecasts show the ash cloud progressively covering the whole of the UK.
"We will continue to monitor Met Office information and review our arrangements in line with that."
The grounding of aircraft began on Thursday morning after a volcanic eruption in Iceland.
The restrictions were imposed because of the danger the ash poses to aircraft.
Tiny particles of rock, glass and sand in the cloud could damage engines.
Flights between Cornwall and Scilly continued until Saturday afternoon, because they do not operate at sufficient altitude to be affected by the ban.
But they were stopped after a Newquay flight reported ash on the plane.
Some low-level flights were continuing to operate between Blackpool and the Isle of Man.
Meanwhile, a group of churchgoers from Hampshire have been stranded in India after their flight back to Britain was cancelled.
The ash cloud was created by an eruption in the Eyjafjallajoekull area of Iceland, which began on Wednesday and is continuing.
It is the second in Iceland in less than a month.
An atmospheric research team from Gloucestershire has been monitoring the volcanic ash cloud, having flown to the edge of the plume in a specially-adapted plane.