Hundreds of people could be involved.
The bank is facing legal costs which could run into the millions as police investigate the allegations against Dr Gordon Bates, who died in 2009 aged 73.
Dr Bates, who was not a Barclays employee, carried out the examinations in Fenham, Newcastle, England.
The allegations relate to young women who were about to start their first jobs as secretaries and clerks.
Solicitor Chris Shaw, who is representing one of the complainants, said it is believed there could be hundreds of people involved.
The Daily Mirror reports that Barclays alerted police earlier this year and has contacted former staff who may have been targeted.
A special police unit has been set up to investigate and the bank said: 'We are doing all we can to help the inquiry'.