The government is planning to allow outsourcing firms to bid for contracts to manage social services for vulnerable children in England – while dropping laws allowing the removal of companies that fail to do the job properly.

A number of firms have expressed an interest in proposals that would allow them to bid for contracts managing foster care and providing other services for children in care.

But Labour says the plans would take away legal provisions that allow councils to remove a firm that has failed to meet national minimum standards. They would also relax the rules governing independent inspections of services that place and monitor children who are looked after by the state.

Concerns have emerged after two of the biggest outsourcing companies in Britain, Serco and G4S, were found to have overbilled the taxpayer by charging to tag offenders who were dead or in prison.

Lisa Nandy, the shadow children's minister, said the latest plans would leave some of Britain's most vulnerable children at the mercy of an unregulated private sector. She has written to the regulatory reform committee, which is considering a draft legislative reform order, urging it to reject the government's plans.

"For the government to consider outsourcing a sensitive service such as foster care to the private sector, when we have just seen with G4S and Serco how a profit motive can have disastrous consequences for the public purse, is madness. The proposals remove many of the checks and balances required to ensure the safety of children whilst introducing the unchecked unpredictability of the market. They should withdraw these proposals now and think again," she said.

Nandy's letter said the reform order would remove the requirement for direct registration and inspection by Ofsted of providers of social work services in England, by amending the provision which imposes it. "It appears to remove the obligation for a national minimum standard relating to the fitness of providers and any mechanisms for removing providers who fail to meet these standards. The implications are potentially very serious and could have a profound impact on the lives of some of the most vulnerable children in the country."

A Department for Education spokesperson said that even though some legal requirements would be removed under government plans, inspections and a national minimum standard for providers would be covered by councils' existing obligations. The DfE said it was "nonsense to suggest that private-sector and voluntary organisations cannot provide good-quality services for children" and that the suggested change in policy was first explored under the last government.

The coalition has enthusiastically embraced such moves. Pilots in six areas where the private sector was involved, inspected by Ofsted, were set up as a response to concerns that social workers were overburdened and unable to dedicate enough time to supporting children in care. The evaluation, published last year, showed mixed results but no better outcomes for children in care.

An evaluation of the pilots by academics from King's College London, the University of Central Lancashire and the Institute of Education found there was limited evidence for relocating public services for children in out-of-home care to the private sector.

The study, published last year in the Children and Youth Services Review, concluded: "While the independent sector is often the setting for innovation, the public sector continues to function as a repository for a wide range of expertise and resources. It is also more likely to offer continuity of knowledge, skills and care and, in this respect, it may be better placed to respond to the uncertainly that characterises the needs of children in out-of-home care."

Officials laid a draft statutory instrument before parliament on 13 May which will be considered by the regulatory reform committee before coming back before parliament to be decided.

Virgin Care, the social work provider that recently took over social care for disabled children in Devon, responded to the government's consultation. It said it had not so far expressed an interest in bidding for future contracts but supported integrating health and social care. Serco is one of the outsourcing firms that may bid for any future contracts, education sources said. The firm is already involved in foster services in Hertfordshire.

Successful bidders would take over assessing children when they come into care, deciding on the right care placement for them and monitoring the placement.

Critics say the changes could also remove accountability through independent inspection and allow potential conflict of interest between private companies' primary duties to their shareholders and their responsibility to children.

Labour claims that the government's proposals leave a potential conflict of interest because the same company would be able to award placements, monitor them and run them.

A spokesman for Virgin Care said: "What we're about is improving services for the people who use them and integrating health and social care. We will have a look at anything that will help us achieve that aim and help us provide services good enough for our own families."

The DfE said: "It is nonsense to suggest that private-sector and voluntary organisations cannot provide good-quality services for children. Arrangements to allow some councils to delegate social work functions relating to children in care were in fact first introduced by the previous government in 2008.

"We want those councils who ran successful pilots to be able to continue to do so and to make the same opportunities available to any council that wishes to use them. Devolved children in care services will be inspected by Ofsted as part of their council inspection."