Dr Laurence Buckman, chairman of the BMA's GPs committee, said the union was willing to work with government on how the idea might be implemented.
But he said: "The rest of the health service and social services and county councils all work by areas, and suddenly we're going to take general practice out of that and that is very difficult to see how you can make it work.
"We think it is going to be very complicated."
He added: "It is going to be very difficult for the patients who are able to get a doctor remotely - for example, how will they get home visits? - and for the patients who are left behind.
"What will happen to their practice if they're destabilised, because some of the younger, healthier patients have gone elsewhere?"
The union says that a mix of patients, some of them not visiting their doctor often, helps general practice to be cost-effective.
It warns that if younger people register near their workplaces, some practices could be left with patient lists mainly composed of those with long-term conditions and complex illness.
Roger Goss, of the campaign group Patient Concern, said introducing competition might help to improve the overall quality of primary services.
"The less successful surgeries will have to work harder to provide a quality service. It's a good thing if the really incompetent surgery goes out of business."
Shadow health secretary Andrew Lansley said: "We've always argued that it was ludicrous for the government to talk about giving people a choice of GP when they restricted that choice based on their postcode.
"This is too little too late."
There are no plans to alter catchment area regulations in the rest of the UK, where they tend to be much bigger, and there is less pressure on GPs' lists.
Mr Burnham is also expected to set out details of how he plans to link hospital funding to patient experience.
Again, this was a policy which was set out in the Darzi review, but is now being promoted as a key plank in the next stage of improving the NHS.
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