Ministers plan to adjust the system in September 2017 and charge health workers for their degrees.
However, in a letter to the Prime Minister, over 20 groups directed by the Royal College of Nursing said it could prevent people from working for the NHS.
The government said the modifications will generate 10,000 more training places.
The change comes as nurses and doctors gather for their yearly conferences.
The RCN conference is on Sunday in Glasgow, and on Monday, the British Medical Association meets in Belfast.
At present, student nurses, midwives and other staff including physiotherapists are eligible to bursaries of £4,500 to £5,500 in addition to the grant of £1,000 each year throughout their training. The course fees are also covered.
Those who are studying for progressive roles, such as district nurses, could also be affected.
But the government has suggested scrapping these and introducing university fees to bring health staff in line with other students.
Ministers have claimed that the move will lead to a rise in nurse students, of approximately 10,000 as the current number of places is capped by two to one.
However, the letter, which has been signed by BMA and the Patients Association, warned that this is a “untested gamble” and insisted that the government should stop the plans and accurately contemplate their effect.
RCN General Secretary Janet Davies said that as nurses spend half of their degree course working in the NHS it amounted, in effect, to “asking people to pay to go to work”.
“It feels very wrong,” she added.
She also voiced a concern about the circumstance of the NHS.
A Department of Health Spokeswoman insisted that the plans for students would lead to more people studying due to the caps being removed.
But she advised those who are apprehensive to take part in the ongoing discussions on the matter.
A Department of Health Spokesman said: “We need more home-grown nurses in the NHS because they do an amazing job caring for patients, but currently two-thirds of people who apply to become a nurse aren’t accepted for training.
“Our plans mean up to 10,000 more training places by the end of this parliament, with student nurses getting around 25% more financial support whilst they study.”
On the wider concerns about the NHS, the Department of Health said the extra funding being provided this Parliament would “transform services”.
