Four out of 10 of those surveyed by MORI said they would be willing to travel outside the UK for treatment.
And just over half said they felt involving other organisations including the private sector would improve the provision of NHS health care.
Just under 2,000 adults across Great Britain were surveyed by MORI in June.
The poll was released on Sunday as the BMA began its annual conference in Harrogate.
During the week, doctors will discuss issues ranging from the problems faced by qualified refugee doctors who want to work in the NHS, to the new GP contract and childhood immunisations.
'Anywhere in the world'
Doctors leaders said the findings showed patients were fed up of waiting for NHS treatment.
They said it showed it was crucial to put more money into the health service so patients did not have to go elsewhere for their care.
On Monday the government is set to launch a scheme where heart patients in England who have waited more than six months can have the choice of where they are treated.
They could have the operation abroad or in the private sector, paid for by the NHS.
A quarter of those surveyed by MORI said they would travel anywhere in the world for treatment, 15% would travel anywhere in Europe and 27% anywhere in the UK.
In January this year, nine people from Ashford in Kent travelled to the La Louviere clinic in Lille, France, for cataract and joint operations in the first use of continental hospitals to provide NHS care.
Dr Ian Bogle chairman of the BMA Council, said the poll findings showed patients were willing to endure considerable inconvenience in order to be treated quickly.
He said: "We must respect their feelings and push for better patient choice.
"We have a national health service and GPs should in theory be able to refer their patients anywhere in the UK for treatment.
"However it is vitally important that we build up our own local capacity."
He said there were also concerns about continuity of care after patients are return from treatment abroad, and added local treatment was the best medical option.
Thinking laterally
He added: "The strength of public support for mixed provision surprised me.
"It shows that it is right to think laterally about how to improve health care.
"However, if the public is placing such faith in mixed provision, we have to make sure it genuinely provides good quality clinical care for the patient and good value for money to the taxpayer.
"The Ombudsman drew attention last week to some deficiencies in continuity of care for NHS patients treated privately under a waiting time initiative."
Mr Bogle said he hoped to meet Health Secretary Alan Milburn to discuss the BMA's concerns over the mixture of services from different providers and the potential impact on staff availability and the long term future of the NHS.