The sheep are pastured by "Registered Commoners"

The crafty animals have also perfected the skill of hurdling 5ft (1.5m) fences and squeezing through 8in (20cm) gaps.

They have destroyed several gardens and even graze on the village park, bowling green, cricket field and graveyard.

The grids were installed 10 years ago after a gardener in Marsden, near Huddersfield, held stray sheep hostage.

Dorothy Lindley, a Conservative councillor in the former textile town on the edge of the Pennine uplands in West Yorkshire, said: "They lie down on their side, or sometimes their back, and just roll over and over the grids until they are clear.

"I've seen them doing it. It is quite clever but they are a big nuisance to villagers.

Sheep are quite intelligent creatures and have more brainpower than people are willing to give them credit for National Sheep Association

"They eat plants, flowers and vegetables in gardens.

"It is soul destroying.

"Registered commoners", who can claim rights of open grazing going back to medieval times, pasture the sheep on moorland owned by the National Trust.

Mrs Lindley added: "What amazes us is they are not frightened.

"When you try to move them on they look at you as if to say it is their patch and you are not right in the head.

"You can shout at them and even if they see a dog they are not frightened.

"Several drivers have had to swerve to avoid hitting the animals and damaged their cars or been given a terrible shock.

The cattle grids are 8ft (3m) wide

"What we really need is more fencing to stop them. But they would probably find another way out before long.

"They must find more tastier morsels down here."

A National Farmers' Union spokeswoman in York said: "We have never seen anything like it.

"We have looked at ways of improving the situation but it is very difficult. The grids are substantial bits of kit."

A National Sheep Association spokeswoman said: "Sheep are quite intelligent creatures and have more brainpower than people are willing to give them credit for."