Staff and customers in the bank were made to get on their knees with their hands held up and were threatened with the baseball bats.
One female member of staff was grabbed repeatedly by the shoulder and the wrist and asked her full name and date of birth by one of the raiders.
Throughout the scene members of the public, including a child, were shouted at aggressively by the assailants, with some appearing scared and others crying.
The ad - entitled ‘Heist’ - was seen at around 9pm one night in August on ITV Player during an episode of Coronation Street.
Seven viewers complained to watchdogs that the ad was “likely to cause fear and distress” without justifiable reason, particularly for those who had been victims of violence.
Others said it was “inappropriately placed” at a time when children could have been viewing.
Royal Mail said the ad was intended to be the start of a wider campaign to highlight the dangers of identity fraud outlined the risks of oversharing on social media, and offered information and services to help people protect themselves.
They said that ID fraud was an area of growing concern in the UK with almost 173,000 cases in 2016, the highest level since records began in 1993, and a 59 per cent increase from 2013.
Royal Mail claimed that the level of violence depicted in the ad was “proportionate” in light of its purpose and was not excessive.
And the firm said it had instructed ITV to only show the ad after 9pm.
ITV said they had not received any complaints about the ad.
But the Advertising Standards Authority (ASA) found the ad to be in breach of rules regarding harm and offence as well as responsible advertising.
An ASA spokesman said: “While we understood that the scenario of a bank robbery was chosen to emphasise the seriousness of the crime, we noted that this was not among the common scenarios in which identity fraud was perpetrated.
“As a result, we considered that consumers would not be able to clearly see from the ad how they could protect themselves, for example by avoiding certain actions that could make them potentially vulnerable to identity fraud.
“We noted the ads’ reference to the Royal Mail’s ID fraud centre, but it did not appear until the very end of the ad, during which time the scenario was presented without explanation or context.
“Furthermore, because the setting of the ad was recognisable and showed ordinary people, including a child, being shouted at aggressively by ‘criminals’, lying on the floor and trying to hide behind furniture, and looking visibly frightened, the impact was heightened and there was an added sense of threat.
“Because of this, we considered it to be reminiscent of other crimes or situations that people may have experienced that extends beyond the bank robbery depicted and therefore could trigger negative emotions for those who had been victims of violence.
“We did not consider that the use of baseball bats made the ad less violent than if knives and guns had been used, as the bats were often shown held in a threatening manner by ‘the criminals’ or positioned next to ‘customers’ heads.
“We understood Royal Mail and ITV’s view that the ad served to highlight a serious and growing crime and to assist customers to find information to protect themselves.
“We noted from the results of the test sample of viewers that the ad may have increased ID fraud awareness for those who had seen it.
“We also noted that Royal Mail had amended the Twitter ad so that a warning appeared accompanying the video and that they did not intend to use the ad again.
“However, we considered that the overall presentation of the ads, as seen by the complainants, was excessively threatening and distressing to the extent that it overshadowed the message the ad intended to convey.
“We concluded the ad was likely to cause fear and distress to viewers, in particular to victims of violence, without a justifiable reason.”
He added: “We told Royal Mail to ensure that in future their ads did not cause fear or distress without justifiable reason.”