Scientists and engineers have agreed a new safe threshold - a concentration of ash of 0.002g per cubic metre of air. At or below this concentration, there is no damage to aircraft engines.
Scientists now believe the worst of the ash cloud has passed - but geologists say the volcano could resume erupting at any time. The end of an eruption is officially declared only three months after the last seismic activity.
Heathrow, Gatwick and London City airports resumed limited flights after being completely closed until 0700 BST. In the Netherlands, Amsterdam's Schiphol, Rotterdam and Groningen airports are closed until 1400 local time (1300 BST).
Flights in and out of Dublin, in the Irish Republic, are also grounded until at least noon
"One side of the airport is clear and the other side, where the final approach track is, actually has a cloud of ash which goes right across final approach," said Nats director Ian Hall.
"So, very frustratingly for everyone, we can't get the aircraft into Gatwick but we can get them out." Eurocontrol, the European air safety body, said Heathrow arrivals would be limited to 30 an hour initially - down from the usual 42 - and it warned of significant delays.
Knock-on disruption was likely to continue throughout last Monday, a Heathrow spokesman said. Meanwhile Network Rail pledged to do everything possible to help stranded travellers make journeys by train.
Virgin Trains said 7,000 extra seats would be made available on Monday, mainly on routes between Birmingham and Glasgow and Edinburgh, and between London Euston and Glasgow
Ash from the Eyjafjallajokull volcano has led to thousands of flights being delayed or cancelled across Europe since April. But after the latest airport closures this weekend, airlines have criticised the amended regulations. On Sunday, Virgin Atlantic president Sir Richard Branson called the closure of Manchester airport "beyond a joke".
"All the test flights by airlines, aircraft and engine manufacturers have shown no evidence that airlines could not continue to fly completely safely," he said.
CAA chief executive Andrew Haines said: "It's the CAA's job to ensure the public is kept safe by ensuring safety decisions are based on scientific and engineering evidence; we will not listen to those who effectively say, 'Let's suck it and see.'"
A spokeswoman from the CAA told BBC News: "Air manufacturers, both engine and airframe, were asked to look at the scientific evidence from test flights and at the Met Office data, to understand how much volcanic ash in the atmosphere… jet engines could tolerate [without being] damaged." Current data suggested that concentrations of ash in UK airspace were around 100 micrograms (or 0.0001g) per cubic metre, explained Dr Grant Allen from the Centre for Atmospheric Science at the University of Manchester.
"Analysis of those atmospheric measurements is early and still ongoing and being supplemented with new measurements all the time," he said.
"Two research aircraft will fly [on Wednesday] to record ash size distributions to assess how near to the new tolerance concentrations actually are, which will also be compared to previous days."
The answer to this is still unclear, but Dr Allen said that early analyses of the research flight data suggested that the plume that had been measured over the past four days contained only 0.0004g of ash per cubic metre at its peak.
