Chris Joseph of Safe, the Struggle against Financial Exploitation, said: 'We're calling this 'the wrongs issue'.'
Mr Joseph said he had had several meetings recently with Andrew Buxton, Barclays' chairman, and Martin Taylor, chief executive. However, his request for a dispute resolution scheme to avoid costly court cases between the bank and customers with serious complaints, had been rejected.
Safe has 2,000 members who have made or are making complaints against their banks, said Mr Joseph. The group was set up in 1992. Mr Joseph, who runs an advertising agency, Hook Advertising, has himself been in dispute with Barclays Bank.
'We will invite people to contact us who have serious issues. We will give them a share certificate and then we will convene and go to the AGM together.'
Safe plans to extend the 'wrongs issue' campaign to other banks, said Mr Joseph.
A spokesman for Barclays said: 'Obviously shareholders have the right to come along to a shareholders' meeting. If they are shareholders they will be admitted.
'We are not sure what they (Safe) will do. They have not contacted us over this.
'If people have specific complaints it would obviously be difficult to respond to them at an AGM. But we will take questions,' he said.
'Christopher Joseph has regularly turned up to shareholders' meetings and asked questions. The AGM is a forum for talking about group strategy and other issues for the bank. Complaints would be better dealt with through the complaints procedure.'