LONDON, April 2 (Reuters) - Sterling hit a three-week high versus the euro and gained on the dollar on Thursday, as the British currency rebounded further after crashing last month amid coronavirus-driven panic on money markets.

The pound was supported by improved risk sentiment on markets, fuelled by rebounding oil prices. 

Analysts say sterling has benefited broadly in recent weeks from co-ordinated action by central banks including the Bank of England to ease a mad scramble for U.S. dollars, the world's most liquid currency seen as a safe haven in times of crisis.

This has eased selling pressure on other major currencies, including the pound.

Stimulus packages by governments to limit the economic hit from the coronavirus pandemic have also helped sterling, although economists are still predicting a huge global downturn.

Dismal factory output data from Britain and several other countries on Thursday provided more evidence of a looming deep recession. 

Sterling was last up 0.9% versus the euro at 87.81 pence per euro, its highest level since March 11.

Against the dollar sterling was up 0.7% at $1.2455. 

In late March the pound slumped to levels not seen for more than a decade versus the euro, while it nosedived to its lowest level since 1985 versus the greenback.

The pound remains down against both the single currency and the dollar since the start of the year, by around 4% and 6% respectively.

"Action by central banks to ease dollar supply has helped sterling to return to calmer waters," said Kenneth Broux, FX strategist at Societe Generale.

"The oil price rally is also positive at the margin for sterling as it correlates with improved risk sentiment."

Broux said disagreement among euro zone members on a stimulus package to help economies through the coronavirus pandemic may also have weighed on the euro relative to sterling. 

(Reporting by Iain Withers; Editing by Kirsten Donovan) ((Iain.withers@tr.com))