Why was Picasso's Child with a Dove allowed to leave the UK?

Why has one of Britain's handful of important paintings by Pablo Picasso been allowed to leave the country? Where were the Art Fund, the National Gallery and Tate Modern when there was a chance to hold on to this sparkling early gem by the greatest artist of the 20th century?

For Britain has apparently let Picasso's Child with a Dove, in a collection in this country since 1924, slip away. Le Figaro in France reports that the Gulf emirate Qatar has bought this much-loved painting for £50m – the same amount paid to purchase Titian's Diana and Actaeon for British museums in 2009. It seems that when it comes to the big national cash layouts, Britain is still a conservative country, holding on to our Renaissance heritage but quietly letting a Picasso vanish without a bang – not even a whimper.

Qatar does not talk about its art purchases. It only emerged this year that in a secret deal in 2011 it bought one of Cezanne's versions of The Card Players for $250m (£162m) – the highest price ever paid for a work of art. Other recent modern art acquisitions by Qatar include major works by Mark Rothko, Andy Warhol and Richard Serra. The state is emerging as the leading buyer of modern and contemporary art and a lot of its business is handled by dealers in Paris, lending credence to Le Figaro's story that it has acquired Picasso's painting of a small child with innocent eyes, a colourful ball and a gentle dove.

In this painting, the artist who was to reveal his inner male violence in paintings of savage bullfights shows his sweet and loving side, a simple joy in life. Child with a Dove is however more revolutionary than it might seem. It has a primitive clarity no 19th-century artist was capable of. Building on the insights of Gauguin, this painting by the young Picasso – it dates from 1901, his 20th year – breaks out into a new visual language of complete boldness and human directness. The dove the child holds would of course become one of Picasso's personal additions to modern symbolism, the dove of peace he was to let fly during the Cold war.

How has Britain's art establishment let this modern treasure flutter away? It seems absurd that so much fuss has been made in recent months about a council's proposal to sell Henry Moore's sculpture "Old Flo" when the UK has many Moores and only a few outstanding examples of the more significant art of Picasso. Losing this painting makes Britain look parochial and stuffy and frankly confused about our artistic priorities. New York's Metroplitan Museum of Art has just acquired 33 works by Picasso. Britain's museums are down one. Is London really serious about its claim to be the new capital of modern art?