Patients are targeted because the survey asks if they remember being offered a choice of hospitals at the time of referral.
GPs fear the software could breach data protection laws, and practices have reported the software extracts data without waiting for staff to select an option.
They fear patients may object to being approached for a survey because of a recent referral, because they have not consented to their record being used.
Joint RCGP/GPC IT committee chairman Dr Paul Cundy said his practice would not be installing the software.
Dr Cundy said the DoH had confirmed that practices could fulfil DES requirements by choosing to have patients contacted via data held on the Exeter system instead.
However, Dr Peter Williams from the Bakewell Surgery in Derbyshire said his patients were signing statements saying they did not want their data uploaded by Apollo. He said practices could mark opt-outs with the Read code 9Nd1. Connecting for Health was unable to comment.
Last week, the GPC told practices in England to consider dropping the DES, worth £12,000 to an average practice, after a dispute with the DoH.