BBG has secured a meeting with the OFT to discuss whether the regulator is willing to apply recently introduced consumer protection legislation to crack down on copycat packaging.
The group has 22 members who are reluctant to be named because they are wary of suffering retaliation from retailers for raising the issue.
According to the group's director John Noble, BBG lost a member in the 1990s because of retaliation after the issue was raised in the House of Lords.
BBG is hoping the OFT and Trading Standards take action in relation to a clause in the Consumer Protection from Unfair Trading Regulations, which were introduced in May 2008.
The clause states that the following is unfair: "Promoting a product similar to a product made by a particular manufacturer is such a manner as deliberately to mislead the consumer into believing that the product is made by that same manufacturer when it is not."
Research carried out by BMRB on behalf of BBG revealed that one in three shoppers admitted to accidentally buying the wrong product because its packaging was similar to that of a well-known brand.
The survey also found that 64% of people interviewed believed that similar packaging suggested a connection that did not exist with a leading brand.
The top three reasons given by shoppers for why they perceive packaging to be similar were colour (79%), overall design (60%) and shape (54%).
BBG said that the use of key elements of the presentation of familiar and trusted brands clearly misleads consumers into believing that the copy actually is the brand or is connected with the brand manufacturer.
Some of the misleading products highlighted in the survey include Asda's 'You'd Butter Believe It' margarine packs, which are very similar to Unilever's 'I Can't Believe It's Not Butter' brand, and Lidl's 'Jammy Rings', which resemble Burton's Biscuits' 'Jammie Dodgers'.
Noble said: "The research proves what we have known for a long time -- products that hijack established brand identities trick consumers into buying them.
"More than ever in these difficult economic times, shoppers need both value for money and the reassurance that comes from buying a brand which they trust will deliver on its promises."
David Haigh, chief executive of Brand Finance, said: "Branded products owe as much to their packaging design as to their brand names.
"Their owners invest vast amounts to differentiate themselves, build consumer goodwill and brand value.
"Copying unfairly expropriates that goodwill and steals value. It is tantamount to theft."