Parents have raised concerns that the children concerned – some as young as 11 – could use the Visa cards to buy goods on the internet without them knowing. According to reports, a 15-year-old boy used the card to buy cheap cigarettes, Viagra and a fake ID on the web before his parents found out.

Previously, 11- to 15-year-olds were issued with a debit card when they opened a current account, but these debit cards could only be used at a cash point or in a bank branch. The Visa-enabled cards can be used anywhere the Visa sign is displayed.

A Lloyds TSB spokesperson said last night: ‘We wrote to customers under the age of 16, who previously had a cash machine card, to let them know they could have a debit card.

“We made it clear that they should let their parents know. Parents or guardians can ask for the cards to be blocked.”

He went on to say: “We don’t always have the parents’ contact details or know the family’s circumstances. There are cases where the child might bank with us but the parent might not.”

“If the card is used on certain website[sic] a Visa flag would come up and the purchase would not go through.”

The bank receives a fee each time a card is used, and the idea that Lloyds is profiting from the purchase of potentially unsuitable goods made by children has been criticised. Liberal Democrat Treasury spokesman Vince Cable said: “It is deeply dispiriting. This is clearly motivated by short-term greed.”

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