NHS staff including doctors, nurses and pharmacists who do not wish to take part in assisted dying will have specific protection against discrimination under a new amendment from the bill’s sponsor Kim Leadbeater, backed by ministers.

Leadbeater, who is hoping to shore up support for the bill before a crucial Commons vote next week, will add the additional protections for any staff involved in the proposed process, including ancillary staff, who will not have to give any reason for their refusal.

The private member’s bill, which faces its next Commons stage next Friday (16 May), currently says doctors and health professionals may refuse to take part.

But the Guardian understands this will be extended to any person who may possibly be involved in the process and will be amended to say “no person is under any duty to participate in the provision of assistance”.

There will also be an amendment to the current Employment Rights Act that will specifically ban discrimination, dismissal or disciplinary action if a person chooses not to participate.

“Choice is at the heart of the bill,” Leadbeater said. “Assisted dying is not for everyone and nor should it be. But for those who do make that choice, the bill that MPs will be debating again in less that two weeks, contains even more protections and is more effective and workable than it was before.”

The amendment from Leadbeater, one of dozens expected to be proposed to the bill at its report stage vote next week, is an effort to reassure medical professionals opposed to the change that they need not take any part in it.

But it is also key to heading off criticism of the potential burden that assisted dying may add to the NHS, which could involve training huge numbers of staff. The higher-end cost estimates in an impact assessment released on Friday found the costs could reach £10m a year within a decade.

But allies of Leadbeater said some of the higher cost estimates should not be seen as the most likely result because some calculations assume all healthcare professional would wish to participate.

Proponents of the change have sought to play down some of the estimates in the impact assessment, which suggested up to 4,000 people a year could access the service, making it 0.7% of all deaths in England within 10 years. But Leadbeater has been pointing out that the central estimate in the impact assessment is half that number, with figures in the early years significantly lower.

Leadbeater said she hoped the change would give reassurance to medical professionals that they had an absolute choice over whether to be involved. She said the impact assessment confirmed “only a relatively small proportion of people would want to exercise that choice”.

She said: “It is a very personal decision, but from all the discussions I have had with people with experience of the injustice and lack of dignity and autonomy in the law as it stands, I know just how important this reform is to those who would want to end their life on their own terms.”

Leadbeater said the amendment was the fulfilment of a promise she had made during the bill’s committee hearings to look again at strengthening the opt-out for people who may be involved in assisted dying

“Nobody will be at risk of any detriment to their careers if, for any reason at all, they choose not to take part,” she said.

“I am firmly of the view that the overall impact of this long-overdue reform will be to make end-of-life care in England and Wales more compassionate and significantly safer. We cannot afford to ignore the injustice and unfairness in the current legal framework and I’m grateful to all those in government who have analysed with such care the impact that this legislation, if passed, will have.”