After surveying 648 applicants about their intentions if their applications are unsuccessful, the BMA found that 55 per cent said they would be likely to seek a training opportunity overseas and complete their whole training there.
Nearly five per cent said they already had offers of overseas post confirmed and 40 per cent said they would look for employment outside the NHS.
Forty four per cent said they would leave medicine and seek employment outside of the medical profession if they do not secure a training post.
The survey comes as MPs debate junior doctors' training reforms in the House of Commons.
Commenting on the survey, Dr Jo Hilborne, chairman of the BMA's junior doctors committee, said: "The NHS could lose thousands of its best young doctors simply because of poor planning. This is not acceptable.
"It's unfair on them, it's unfair on their patients, and it's unfair on the taxpayers who've funded their training.
"These changes have caused anxiety on a massive scale, and we are concerned about their impact on patient care as well as doctors' morale. We want to discuss ways of addressing this with the health secretary."
Shadow health secretary Andrew Lansley added: "Junior doctors have been systematically undermined by this government's failure to implement an open, fair and effective selection process for training posts. Patients will ultimately lose out as some of our most talented and skilled doctors are forced to seek opportunities overseas and out of the profession altogether.
"Unless strategic solutions are provided as a matter of urgency, the future of NHS care is at stake. I will be pressing the government on this issue again in parliament."
Responding to the survey, a spokesperson for the Department of Health (DoH) said there will "always be competition" for speciality training posts as they are very highly skilled.
"But these are only training posts, and there are still jobs in the NHS for junior doctors who don't get a training place," the spokesperson said.
"We want our doctors to progress and develop their careers in the NHS where we see them as our doctors of the future. There are many options open to applicants who do not secure a training place, including trust grade posts in the NHS, locum work, or spending a period of time working outside the NHS.
"However, it's not unusual for doctors to either work abroad or travel and Australia and New Zealand are favourite destinations. The majority of those who go abroad come back to England to continue their careers in the NHS, enriched by their overseas experiences."
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