The doctor's union said a petition calling for the government to support existing GP practices and urging it to end plans to encourage private firms into primary health care received 1,196,000 signatures in three weeks.
The petition is due to be handed to Prime Minister Gordon Brown later on Thursday and Dr Laurence Buckman said it would give him a "stark message".
"Voters don't want funding to move from GP practices to commercial companies who are accountable primarily to shareholders rather than patients," Buckman will tell a doctors' conference.
"They want to be treated as patients, not customers. My message to Gordon Brown is this: Whatever you think of GPs, take note of what your electorate thinks."
The government wants every local authority to build at least one polyclinic, grouping together a team of family doctors with nurses and other health services, and open seven days a week from 8 a.m. to 8 p.m.
The polyclinic programme is being led by Health Minister Lord Darzi, a leading surgeon brought into the government last year by Brown to drawing up a blueprint for the future of the NHS, which celebrates its 60th anniversary in July.
Darzi's plans would mean about 150 "health centres" being built to complement existing GP services. However the BMA argues such large clinics would break the traditional relationship between patients and their GP.
Last week health think tank The King's Fund said polyclinics would not by themselves improve the quality of healthcare provided to patients.
The King's Fund warned that a major centralisation of GP services into a small number of polyclinics would make it harder for patients to see their GP, especially in rural areas.
The government has promised that polyclinics will not be imposed where they are not wanted and has accused the BMA of painting a distorted picture of its plans.
