Academies and free schools in England may be allowed to give priority to the poorest pupils when allocating places, under a new proposed admissions code.
The rules, published for consultation, also allow all schools to give priority to teachers' children.
The government said it wanted a simpler, fairer code and it would let good schools expand more easily.
But teaching unions warned the changes would "create another generation of haves and have-nots".
The admissions code covers entry to all state schools, most controversially, the basis on which places are allocated in popular, oversubscribed schools.
School admissions remain highly competitive in some areas, with one in seven pupils failing to get a place at their first choice of secondary school this year.
There are also concerns about a shortage of primary school places in the next few years in some areas, with London predicting a shortfall of about 70,000 over the next four years.
Education Secretary Michael Gove said the old code, which was 130 pages long, was "bureaucratic and unfair".
The new version is just 50 pages, and includes a range of changes he said would help "give all children the chance of world-class schools".
The proposals include:
- Allow free schools set up by parents and community groups, and academies - state schools outside local authority control - to give priority to children eligible for free schools meals (those whose parents earn less than £16,000 a year)
- Allow schools to give priority to the children of their own teachers and other staff, something which was stopped under Labour
- Allow popular schools to expand without permission from local authorities or the education secretary
- Allow primary schools to increase infant class sizes beyond 30 pupils in order to take in twins and children whose parents are serving in the armed forces
- Remove the explicit ban on admissions authorities drawing catchment areas and selecting feeder schools in such as way as to disadvantage children from deprived areas
- Ban local authorities from using area-wide lotteries
- Alter the appeals process to make it "cheaper and less burdensome"
- Improve the way places are allocated to children who move area in the middle of an academic year
Mr Gove says the existing system needed to change because it "rationed good schools" and with wealthier families able to go private or move house, "the poorest are often left with the worst schools".
"Good schools should be able to grow and we need more of them," he said, having argued earlier in the week that allowing popular schools to expand more easily would increase the amount of good school places.
Journalist Toby Young, who is setting up one of the first free schools, said he would want his governors to take advantage of the proposal to allow schools to set aside places for pupils on free school meals, if it is implemented.
He said the idea was welcome for free schools and academies that were "worried about places being monopolised by middle class children".
'Spiral of decline'
The Association of School and College Leaders (ASCL) said the proposals would not improve social mobility and would have a "damaging effect" on pupils from the most deprived areas.
In April, the coalition's "pupil premium" came into effect, under which schools receive an extra £430 per year for every pupil on free school meals that they teach.
ASCL general secretary Brian Lightman said this would "hardly be enough of an incentive or a supplement for schools to provide the additional support that these pupils so often need".
And allowing popular schools to expand would "create another generation of haves and have-nots".
"Those schools left with the most challenging pupils, who need the most intensive support, will suffer a slow spiral of decline and their pupils will lose out on life chances," he said.
And the NASUWT teaching union pointed out that the rules would allow grammar schools to expand without having to run local consultations.
"Forget about selection by the back door. This is selection by the front door," said general secretary Chris Keates.
Separately, the government said that it would, on a case by case basis, consider allowing free schools set up by parents to give priority to the children of those who founded them.
This is not included in the new code, but would be written into each school's funding agreement with the government.
Coalition ministers have long said they wanted to shorten and simplify the existing code.
Outgoing chief schools adjudicator, Ian Craig, said he was "pleased" at the publication of the new code.
"Reducing the complexity and making it easier for parents to understand without removing the safeguards for vulnerable groups is essential to our admissions system," he said.
He had warned in November that slimming down the code could risk "throwing the baby out with the bathwater" and reducing it to "a useless document".
The government is also altering the school admissions appeals process in the Education Bill currently before Parliament.
The Bill would limit the Office of the Schools Adjudicator to investigating specific complaints, rather than wider issues where it suspects there may be a problem.
The body would, however, be able to accept complaints from a wider range of people and its remit would be expanded to cover academies.
The government says this will reduce bureaucracy without affecting fairness, but Labour has warned that such changes could result in reduced scrutiny and an increase in "selection by the back door".