In total the authority overpaid more than £3.5 million to households in 2011/12, but managed to recover £2.9 million of that figure. This meant a total of £208,597 was eventually written off by the authority, which ruled that it would cost too much for it to try to recover the money.

Councillor Martin-Taylor Smith, the council’s head of transformation and IT, said the overpayments were mainly caused by changes to claimants’ circumstances, such as rising or falling income or a change of address.

He said the complexity of the benefits system, which he said Einstein would struggle to understand, was also a factor, and he welcomed Government plans to simplify the method of making payments.

“Writing off anything, as any business will tell you, is not something you do lightly,” Councillor Taylor-Smith added.

“Eventually a judgment call is taken. Throwing good money after bad comes to mind.”

He said the council had already cut overpayment rates and would continue to do so.

He added: “Recovery of overpayments is resource intensive and cannot always be guaranteed.

“While every effort is made to recover funds, in some circumstances it is not possible to recover funds, or it is not justifiable economically to continue recovery procedures.

“In these instances we carefully consider if an overpayment needs to be written off.

“Typical examples would include where a claimant has died, absconded without trace or has been declared bankrupt.”

Shropshire Council has 25,000 claimants for housing and council tax benefit and pays out £80 million each year.

Earlier this year it was revealed that cheats had falsely claimed more than £420,000 in housing and council tax benefits.