The secret filming showed a trainer telling employees to ignore the wishes of customers who had stated that they did not wish to receive sales information or be contacted by telephone, which the ICO views as "totally unacceptable".
In addition, the programme showed that call centre marketing staff were told to identify themselves as "account consultants" when speaking to customers instead of using their normal title of "sales adviser", and also showed staff accessing customers' accounts without a valid reason.
The ICO said the investigation will establish if Barclays has breached the Data Protection Act and the Privacy and Electronic Communications Regulations.
It has requested the bank supply it with materials including: the results of its internal inquiry into the matters raised by the BBC; a copy of its policies and procedures with regard to telephone sales protocols; and an explanation outlining why its procedures "appear to have been deliberately flouted" by call centre staff.
Mick Gorrill, head of the regulatory action division of the ICO, said: "We will report publicly on this investigation once it is completed."