Parts of European airspace re-opened this morning and the first new flights started to take off:
Planes have been departing from Paris, Madrid, Amsterdam and Frankfurt - though many flights are cancelled.
There are hopes that many routes within Europe will be able to resume operations on Tuesday.
But UK air traffic officials said a new ash cloud spreading from Iceland cast doubt on plans to reopen UK airspace.
The UK's air traffic control authority, Nats, says it is unlikely that the main airports in London will reopen on Tuesday, because of more ash in the atmosphere.
Flights have taken off from Scotland and there is limited airspace over the north of England. British Airways says it has cancelled all short-haul flights