Professor Paul Stanton, director of the board development team at the NHS clinical governance support team, urged boards to plan for the bill.
It will hold trusts criminally liable for deaths on their premises where there is a 'gross breach of the relevant duty of care'.
The bill, which needs to get royal assent by 17 July or will be abandoned, removes immunity from the NHS and trusts will be considered as corporate bodies.
Professor Stanton said: 'The individual executive and non-executives will not be prosecuted but they may have to appear in the dock in a criminal court of law. The sentence will be a fine but the real risk is to the reputation of the organisation and the board members.'
He said trust boards should be looking at the quality of assurance that it has in relation to safety and quality of all provision.
He added: 'A board has two statutory duties: one is quality and the other is care, not just care of staff but of anyone who uses services. The duties are extremely onerous in themselves and the bill adds an additional sharp edge to potential liability in what is already a high-risk area.'
He said the bill could have been invoked in the case of Southampton University Hospitals trust in 2000, when a 31-year-old man admitted for a routine knee operation died from a bacterial infection which two doctors failed to diagnose and treat.
The doctors were convicted of gross negligence manslaughter under the Health and Safety at Work Act 1974.
'Had the bill been in place it could have been a criminal proceeding rather than a civil one,' he said.
David Frith, a partner at law firm Capsticks and lead on the implications of the proposed new law, said: 'The bill states that the fine is unlimited, and an indirect consequence of any fine would be a stigma attached to those found to be a corporate killer. This would in turn have implications in recruitment and retention, and chief executives could find themselves in a compromising position.'
He added: 'The government is looking at the bill as introducing no new burdens if corporations comply with health and safety requirements they cannot be liable under corporate manslaughter. But it is an immense undertaking to review policy and procedure and check that staff are properly supervised and trained.'
The bill is passing back and forth between the Lords and the Commons due to the government's wish to exempt deaths in custody.
A compromise where deaths in custody will not be included but introduced at a later stage is being looked at.