Ministers want to tackle the class divide in society
Public bodies could be legally required to tackle social inequalities in their policies under plans which the Tories say look like "class war attacks".
Equalities minister Harriet Harman is to consult on whether to legislate to oblige government and councils to help those from disadvantaged backgrounds.
It forms part of government efforts to widen opportunities for people and raise levels of social mobility.
The Conservatives said the idea "missed the point" of what caused inequality.
Ministers are looking at requiring public bodies to recognise and tackle inequalities stemming from social background in the same way as they must already do for race, gender and disability.
Class was still the source of "persistent inequality" in British society, the government said in a white paper on social mobility published on Tuesday.
Announcing a consultation process on what public bodies could do to enhance social mobility, ministers said they had a "crucial role" to play in helping people fulfil their potential.
"Given the important role public policies and services play in supporting individuals to make the most of their talents, we will consider legislating to make clear that tackling socio-economic disadvantage and narrowing gaps in outcomes for people from different backgrounds is a core function of public services," the white paper stated.
Ministers said they had not reached a "definitive conclusion" on the best way forward.
However, one option under consideration is including a legal provision on public bodies to act accordingly in the Equalities Bill currently before Parliament.
The bill, designed to increase fairness and diversity in the workplace, would also allow firms to discriminate in favour of female and ethnic minority candidates and require public bodies to disclose the extent of any gender pay gap in their organisation.
It is not clear whether public bodies, such as government departments and local authorities, would be allowed to discriminate on grounds of family or educational background in their recruitment policies under the new proposals.
However, they could be required to direct resources to areas most likely to reduce income inequalities such as health campaigns and school spending.
The proposals are being driven by deputy Labour leader Harriet Harman who will say in a speech on Saturday that Labour wants to "tackle the class divide", not merely "just provide escape routes out of poverty for a talented few".
But the Conservatives said the proposals reflected a reversion by Labour to class-based politics.
"Harriet Harman's attempts to play up to the left-wing gallery look like a return to the class war attacks of the Crewe and Nantwich by-election," said shadow equality minister Theresa May.
Labour was accused of making the background of the successful Conservative candidate in Crewe an election issue, a tactic some ministers agreed was counter-productive.
The new proposals were a "box-ticking" exercise rather than a real attempt to extend opportunity to more people, Ms May added.
"You don't make people's lives better by telling them they have a legal right to a better life. You do it by tackling the root causes like family breakdown and poor education."