Atlantic bluefin tuna: Sienna Miller and Stephen Fry among those credited with raising awareness of overfishing danger

The clearest signs of a recovery have been seen in the eastern population

Celebrities who have campaigned for Atlantic bluefin tuna to be kept out of the cooking pot may soon have to find a new fish to champion after scientists concluded the species is on the mend.

Sienna Miller, Greta Scacchi, Elle Macpherson and Stephen Fry are among the stars to have called for an end to the overfishing that was devastating stocks.

Scacchi went so far as to pose naked, along with Emilia Fox and Terry Gilliam, while holding strategically placed fish, in the name of conserving the bluefin.

Their hopes of seeing the fish recover in the Atlantic and even in the drastically overfished Mediterranean now seem realisable with the World Wide Fund for Nature (WWF) declaring that the fish is “no longer at risk of collapse”.

Populations remain at historically low levels, but for the first time in decades conservationists, scientists and fishermen seem unanimous in agreeing that the numbers of Atlantic bluefin tuna are rising.

Dr Sergi Tudela, head of fisheries for WWF Mediterranean, was buoyed by the findings. “In spite of the high uncertainties surrounding the assessment, one thing appears clear today: the stock is no longer at risk of collapse, and this is a direct result of the current recovery plan,” he said.

The numbers of bluefin tuna are rising – but consumers are still advised not to eat them (Gavin Newman/AFP/Getty Images)

“We might be very close to what would be a resounding success in the history of fisheries, the dream of a sustainable bluefin tuna fishery in the eastern Mediterranean and the Atlantic – let’s hope the lessons of the past have been fully learned.”

There are two distinct stocks of Atlantic bluefin tuna: the bigger in the eastern Atlantic, including the Mediterranean; and the smaller in the western half of the ocean, including the Gulf of Mexico.

The clearest signs of a recovery were seen in the eastern population. Shana Miller of the Ocean Foundation said the evidence suggested “the population has grown significantly and is on its way to recovery”.

For the western population the improvement has not been so marked, but there has nevertheless been “measurable growth”. She said strict limits on the fishing quota have been “beneficial to the stock”.

Conservation groups caution, however, that while the rise is immensely welcome, it is only the start of recovery. The Marine Conservation Society in the UK and WWF across Europe still advise consumers and the catering industry to avoid buying and eating bluefin.