White storks nesting on top of an ancient oak tree could become the first wild pair to successfully breed in Britain for hundreds of years.

The enormous birds are brooding three eggs on the rewilded Knepp estate, in Sussex, as part of a project to reintroduce the species to south-east England.

“It’s absolutely thrilling,” said Isabella Tree, the author and estate’s owner with her husband Charlie Burrell. “She is sitting on three eggs and we feel like parents – after torrential rain we rush out to see if their nest is still there.”

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The Knepp estate is close to the West Sussex village of Storrington, referred to as Estorchestone or “homestead of the white storks” in the Domesday Book. Although the occasional wild stork flies across Britain, the birds are believed not to have successfully bred here since 1416, though some believe wild storks fledged chicks as late as the English civil war.

The storks have been brought back in a collaboration between three landowners in south-east England, the Cotswold Wildlife Park, Warsaw Zoo, the Roy Dennis Wildlife Foundation and the Durrell Wildlife Conservation Trust, an expert in restoring endangered bird species.

Birds with clipped wings from sanctuaries in Europe were introduced into large, fox-proof, open-topped pens three years ago. Conservationists hoped these would attract passing wild storks, which has happened.

Additional birds bred in captivity will be released over the next five years, with the aim of a self-sustaining wild population by 2030.

Ros Kennerley, the UK programmes manager for the Durrell Wildlife Conservation Trust, said: “They are not globally endangered but they are a really charismatic large bird that symbolises rebirth and which people can see. They can be a means to inspire people about the natural world.”

Within weeks of being released into the pens at Knepp, one bird had defied its clipped wings to take flight and escape, and was subsequently spotted in Norfolk, Hampshire and Dorset.

One of the fears with the project was that British-reared birds would not be capable of flying to continental Europe and mixing with wild populations there, nor undertake the migration to spend the winter in sub-Saharan Africa.

Omnivorous storks stalk through grassland eating small mammals, snails, crickets, earthworms and large insects. Conservationists believe there may be enough winter food in southern England for the wild birds but other reintroduced birds in Europe have begun to migrate. At Knepp, the individual that flew free went on to travel across the Channel to Brittany, and has since returned to the estate.

Tree said: “Even with clipped wings this one bird went rogue almost immediately, spent time on the Isle of Wight and picked up a potential mate which was eaten by a fox. It flew off to Brittany but it’s now back in the Knepp pen which is really exciting because it shows that migration is possible – that the birds can go off to Europe and back to Britain.”

Storks’ habit of building huge nests and faithfully returning to them each year has seen them play an important role in history, culture and folklore across Europe.

The Greeks created the myth that storks delivered newborn babies and nesting storks are widely seen as heralding good luck in traditional European cultures. Storks have also been used as symbols of rebellions against oppression. Their former status in Britain is mysterious – they may have been expunged during the Reformation – but it has also been claimed that the last breeding pair nested on St Giles Cathedral, in Edinburgh, in 1416.

Successful reintroduction programmes have returned the birds to France, Poland, the Netherlands and other European countries where wild populations now build their enormous nests on chimneys or special platforms in villages and towns.

Despite erecting nesting platforms for them at Knepp, the birds chose to construct their own large nest on top of an oak tree.

The eggs in the first nest are due to hatch next month but Tree cautioned that the pair were young birds and may not yet have mastered parenthood.

“They are juveniles and it’s all very uncertain,” said Tree. “We watched them poking around with twigs and fighting over where to put a twig and we thought they were never going to build a nest, but it just grew like magic. Who knows if they will fledge chicks successfully but it’s lovely to see them back flying free.”

• This article was amended on 23 May 2019. An earlier version neglected to list the Warsaw Zoo and the Roy Dennis Wildlife Foundation as partners in the project.