Children as young as two were offered £20,000 loans following a mail-out blunder by the Abbey National.
A brother and sister aged two and four from Sutton Coldfield received the letter offering them the loan because they had Smart Saver accounts with the bank.
Their father contacted the Abbey National and claims he was not even offered an apology.
"The letter asked if my children wanted some extra cash to improve the house, saying it couldn't be easier to borrow money. It said just pick up the phone or visit your Abbey branch," he said.
"I rang them up and was just told it was a national mailshot that had gone to everybody under 18 by mistake.
"I was concerned that they were not using clients' personal data for a fit purpose."
A spokeswoman for the Abbey National said the letters were supposed to have gone to the children's parents.