A family of wild beavers has been seen in the English countryside in what is believed to be the first sighting of its kind in up to 500 years.

Three European beavers (Castor fiber), believed to be adults, have been filmed together on the River Otter in east Devon and can be seen gnawing at the base of trees, grooming themselves and playing together.

Experts said the sighting was "highly significant" as it strongly suggested a small breeding population of beavers now existed outside captivity.

European beavers were once widespread in the UK but were hunted to extinction by the 16th century in England and Wales for their fur, medicinal value and meat.

There have been successful reintroduction schemes in other parts of the UK. In 2009, three beaver families were released into forest lochs near the Sound of Jura in Argyll, while plans to release the species into the wild in Wales have also moved a step closer. The sighting in Devon would be the first time in centuries that European beavers have bred in the wild in England.

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The footage was captured by local retired environmental scientist Tom Buckley, who noticed some trees had been felled in the area in late last year. Together with landowner David Lawrence, he installed three motion sensor cameras along a 400-500m stretch of the river. A lone beaver was spotted on the farm in January and last July a woman claimed she saw a beaver on the river.

"We'd seen bits of trees chewed and cut down and I was starting to think that it was a sign of beavers even though I couldn't believe it," Buckley said.

Beaver expert Derek Gow confirmed that one of the animals filmed by Buckley was a juvenile and the family may have been in the wild for years. Buckley does not know where they have come from or exactly where their home is.

"When I first saw that first beaver it was such a shock. When I saw three it was slightly different – we knew there was one around and we were tracking its activities. When we watched film and all of a sudden another appeared, and then another – I would not just say that was amazing – one was speechless realising what was happening. We had no idea there was more than one, and they are all quite large and active as well."

Devon Wildlife Trust has been running its own Beaver Project since 2011, when an adult male and female were introduced to a securely fenced compound in the north-west of the county.

But the beavers remain in their compound and are not the source of the population now seen on the River Otter.

Steve Hussey from the Devon Wildlife Trust said he supported the reintroduction of beavers to England but that it had to be "properly planned".

"In principle, we would like to see the European beaver reintroduced to England but recognise that a great deal of work needs to be done before this can happen."

He said the beavers should be left alone and observed using a rigorous monitoring programme.

"This group of beavers provides us with a unique opportunity to learn lessons about their behaviour and their impact on the local landscape … [the group] could contribute to this process if they are subjected to thorough scientific study.

Beavers are a "keystone species", meaning they provide more important ecosystem services than their numbers alone would suggest. Known as "ecological engineers", their dams, burrows and ditches and the branches they drag into the water create habitats for a host of other species. Their dams slow rivers down, reducing scouring and erosion, and improving water quality by holding back silt.

During the recent wet weather and flooding crisis, naturalists called for the reintroduction of beavers to control floods.

Otter tracks and spraint was found alongside the beaver prints, indicating they may have been interacting with wild otters too.

Hussey added: "There's evidence that otters, beavers are coming together here face to face perhaps for the first time in two or 300 years."

The Department for Environment, Food and Rural Affairs (Defra) is investigating the sighting as it is against the law to release beavers in England. A spokeswoman said the department would "look into this case and will consider what action to take".

She said she could not comment on whether the beavers could be removed from the site or destroyed.

Buckley said: "This beaver family has been around for at least a couple of years and no one seems to have noticed them. They haven't caused any trouble for anybody and it's only because they've been caught on camera that people know they are here. To think about destroying them is totally out of order. This is an insight into what the potential impact is if they are already in a place and at the moment that impact would seem to be zero."