Social workers says children's right to privacy needs to be protected.
The media will be able to report legal proceedings in family courts as part of sweeping changes proposed by ministers.
Cases heard in family courts, such as divorce and custody, will be open to the media subject to some restrictions such as not identifying those involved.
Justice Secretary Jack Straw said the changes would help "lift the veil" on how the legal process worked.
Campaigners, including a senior judge, have challenged current arrangements in family courts as being too secretive.
The Tories said greater transparency of the workings of family courts was needed to protect vulnerable children but that serious questions remained about how the proposals would work.
The proposed changes would bring procedures in family courts at all levels into line with youth courts where reporting of proceedings has been allowed, subject to certain restrictions, for some time.
They follow government consultations on changes last year.
Mr Straw said it would improve accountability and boost confidence in a justice system which had, due to reporting restrictions, been open to accusations of "bias".
"The overall effect of these changes will be fundamentally to increase the openness of family courts while protecting the privacy of children and vulnerable adults," Mr Straw said.
Laws will remain in place to protect children and people's identity in the most sensitive cases, such as those where children face being taken into care.
However, restrictions on naming social workers and doctors who give evidence would largely be eased.
There would be a dispensation to relax reporting rules in the event of a case of major public interest, although reporters could still be excluded if it was deemed in the interest of a child's welfare.
The proposed reforms follow criticism from parents who say social workers took their children into care on the basis of flimsy and unsupported evidence.
MPs have complained the current rules allow some councils to remove children from their parents in order to meet "adoption targets."
For the Tories, shadow justice secretary Nick Herbert said too much secrecy often led to "poor decision-making".
But he expressed concerns about the impact on children of admitting the media, what sanctions would be put in place to those breaking the rules and whether third parties would also be admitted.
Britain's most senior family court judge has argued that opening up family courts would prove to everyone that justice was being done.
Sir Mark Potter, president of the Family Division of the High Court, has said considered reporting could "do nothing but good for the system" and help dispel "myths and inaccuracies" over judgements.
But many social workers are likely to oppose changes that could see often sensitive court proceedings open to press scrutiny.
The British Association of Social Workers has expressed concern that families' fundamental right to privacy will be sacrificed on the assumption that more openness will raise judicial standards.
Adoption hearings will remain closed pending a government review on future options.