The owners believe the two tortoises, Basil and Archie, could have been hidden in a child's buggy or a picnic box before being carried out of the farm.

Now they fear the mating pair, who live at Rand Park Farm in Wragby near Lincoln, could be sold off as pets on the lucrative black market.

Tortoises can fetch large sums as restrictions on importing them have increased their value in recent years.

Cool box

Kay Waring, who runs the farm with her husband Richard, said they never expected anyone to walk off with one of their animals.

"Somebody probably came along with a child's buggy, with the child walking.

"It would be very easy to put the tortoises in the buggy and put a T-shirt on top and walk out.

It never entered our heads that anybody would pinch a tortoise

Kay Waring

"They could have put them in a cool box and carried them out."

She said they believe the pair, who have been mating for three years and have a combined age of 100, were taken between 1400 BST and 1530 BST on Sunday.

The tortoise area would have been untended as the lambs were being fed, said Mrs Waring.

"It never entered our heads that anybody would pinch a tortoise."

Tortoises can fetch hundreds of pounds because of the import restrictions.

Police have asked people who may have been offered any tortoises to come forward.