Ministers have modified the Human Tissue Bill following fears it would compromise medical research.
Tissue is needed for research
Scientists were concerned that the Bill would have outlawed the use of any human tissue for research without a patient's explicit consent.
They feared this would lead to a shortage of tissue, and stymie efforts to develop new ways to tackle disease.
The amendment will mean scientists can assume tissue taken from living patients can be used for research.
Patients who do not want their tissue used in this way will have to make their feelings explicit, or else consent can be presumed.
However, the Bill will also stipulate that scientists can only use the tissue samples if they ensure that they will not lead to the patient being identified, and so long as the research has been officially approved.
It is estimated that 150 million tissue samples are taken each year during medical operations and procedures.
The Bill will still require consent from a patient's will or their family for tissues and whole organs to be removed and retained after they die.
The Bill was created to prevent future organ retention scandals such as those seen at Alder Hey Children's Hospital in Liverpool.
In its original form, scientists who failed to seek explicit consent to use tissue for research would have faced a prison sentence of up to three years, and an unlimited fine.
But the scientific community argued that the approach was unnecessarily Draconian.
Concerns taken on board
The Department of Health said it had listened to the research and medical
community and sought to retain a balance between patients' rights and preventing
another Alder Hey.
Health Minister Rosie Winterton said: "The purpose of the Human Tissue Bill
continues to be to protect the rights and expectations of patients and families,
whilst ensuring a framework in which research can flourish.
"Following representations made during the Committee Stage, and by members of
the scientific and medical research communities, the government has tabled a
number of amendments to the Bill which address the key issues of concern whilst
maintaining the underlying principle of consent."
Dr Mark Walport, director of the Wellcome Trust, said : "We are delighted by these amendments.
"We now have a proper and sensible balance between protecting the rights and confidentiality of patients and their families, and the need to safeguard research that will provide benefits for health in the future."
Professor James Underwood, president of the Royal College of Pathologists, said: "The amendments will make this new legislation feasible, and will enable patients and the public to continue to benefit from medical education, training and research using lawfully removed tissue that would otherwise be discarded or remain unused."
However, Professor Underwood said further amendments, or separate legislation, were needed to assure bereaved families that they will be informed about tissue retained from coroner's post-mortems.
The Medical Research Council said it was studying the implications of the changes.
The Bill is due for a third reading next Monday.