The act, uncovered by the BBC's Watchdog programme, is in breach of an undertaking to the ICO signed by HBOS earlier this year after it was found throwing out documents containing customer details.
The ICO is conducting an audit of HBOS and its security procedures and will soon examine the evidence gathered by Watchdog. If a breach is found then it will serve an enforcement notice on the bank. A repeat offence in breach of the notice will be a criminal offence and will open HBOS to prosecution.
"This was one of the banks that signed the undertaking last year," said an ICO spokeswoman. "If they are found to be in breach of that then the next step will be enforcement action.
"An enforcement notice would outline what they needed to do, ordering them to make sure they have the procedures in place to make sure it doesn't happen again. If it does it is a breach of an enforcement notice," she said.
Watchdog reporters said that they found torn up bank statements which revealed customer names and account numbers and a complete, untorn cheque for nearly £1,700 in a bin outside a branch of Halifax.
HBOS apologised in a statement. "We're very sorry for any inconvenience we've caused. All of the relevant authorities, including the Information Commissioner and Financial Services Authority (FSA), were informed immediately."
"We process over 100 million transactions through our branch network every year. This incident, which is clearly regrettable, needs to be viewed within that context. Following the approach from Watchdog, we're reviewing our procedures again," said the bank.
HBOS chief executive Andy Hornby signed the ICO undertaking after it was found by the ICO to be throwing documents which identified customers and their banking details into ordinary bins. The ICO said that this was a breach of the Data Protection Act.
"[HBOS will ensure that] adequate and relevant data protection training [will] be given to all employees including emphasis on the importance on [sic] confidential secure waste disposal," read Hornby's undertaking. "Customer facing outlets will be equipped with secure lockable bins for confidential waste disposal." The undertaking said that all lockable bins and shredders should be deployed by 28th February this year.
The ICO can audit organisations to ensure their procedures are adequate to protect people's privacy, but must have the permission of the organisation first. Commissioner Richard Thomas last week called for increased powers, asking Parliament to give him the right to audit organisations even when not given permission.