It does not necessarily mean there will be airspace closures but makes flight disruption more likely,it said.
The cloud is predicted to affect parts of Scotland,Northern Ireland and the Republic of Ireland.
The event comes a year after ash from the Eyjafjallajokull volcano spread across Europe,causing huge disruption.
Vast area
The Met Office,which runs Europe's Volcanic Ash Advisory Centre, earlier said there was a possibility of ash moving across the UK towards the end of the week.
But a spokesman said the weather was much more changeable than at the time of last year's eruption and there was a lot more uncertainty.
The Civil Aviation Authority and the UK's air traffic control service Nats said they were monitoring the situation closely.
The Grimsvotn volcano, which began erupting on Saturday, is still active although the plume, at about 8 miles (13km) high, is not as powerful as it was.
By the early hours of Tuesday morning the cloud is expected to cover a vast crescent across the North Atlantic from northern Russia to the British Isles.
During last year's eruption UK airspace was shut down completely by the authorities as a precaution but this time airlines will make their own decisions about whether it is safe to fly.
The National Airspace Crisis Management Executive is meeting every six hours to assess the situation.
Different scale
Icelandic air traffic control has created a no-fly zone around the volcano and cancelled all domestic flights.The country's main international airport, Keflavik airport,has been closed.
The Grimsvotn volcano lies beneath the ice of the uninhabited Vatnajokull glacier in south-east Iceland. The latest eruption is its most most powerful eruption in 100 years.However, University of Iceland geophysicist Pall Einarsson said the eruption was on a different scale to the one last year.
"It is not likely to be anything on the scale that was produced last year when the Eyjafjallajokull volcano erupted," he said.
"That was an unusual volcano, an unusual ash size distribution and unusual weather pattern,which all conspired together to make life difficult in Europe."
The ash particles from this eruption are said to be larger than last year and, as a result,fall to the ground more quickly.
Iceland has been badly affected by the current eruption, with ash falling across the country including the capital Reykjavik.
Tourists have been evacuated from the country's main national parks and farming has been hit.
