An expansion of grammar schools in areas which already have a large representation of selective schools is likely to lead to "small but growing attainment losses" for those not attending selective schools, research by the Education Policy Institute (EPI) shows.
This would be greatest among poor children, who are already under-represented at grammar schools, the independent research body said.
The gap between children on free school meals (FSM) attaining five A*-C GCSEs, including English and maths, and other children is 6% wider in selective areas than in non-selective areas, the study found. FSM pupils in selective areas who do not attend grammars perform worse than the national average.
But the EPI found that, at a national level, there did not appear to be a significant attainment penalty from not attending a grammar school.
David Laws, EPI chairman, said: "It is clear from our analysis that creating additional grammar schools is unlikely to lead to either a significant improvement in overall education standards or an increase in social mobility.
"Indeed, without far more success in getting poor children into grammar schools, the total attainment gaps between poor children and richer children could well increase."
Mr Laws continued: "Our analysis shows that there is a risk that in those areas with large numbers of selective places, more grammar schools will, on average, reduce the results achieved by poorer children."
The EPI warned that it would be "very challenging" to significantly improve grammar school access for poor children as 60% of the attainment gap takes place before the age of 11, when children sit the entrance test.
The resources which might be used to create additional grammar schools could be deployed to help create high-attaining non-selective schools, which are much more socially representative than grammars, it suggested.
The first generation of academies sponsored by Labour are now helping to educate around 50,000 FSM children, the organisation said, compared with 4,000 in grammar schools.
The report, Grammar Schools and Social Mobility, focused on attainment at Key Stage Four (GCSE level), using data from the school performance tables, the School Census and the Department for Education's national pupil database.
The EPI will continue research to see if these findings hold true at Key Stage Five.
Education figures urged the Government to abandon its "disastrous" and "misguided" plans in the wake of the report.
Mary Bousted, general secretary of the Association of Teachers and Lecturers (ATL), said: "This report could not be more timely, and its conclusions could not be more devastating for the Government - that there is no evidence that overall educational standards in England would be improved by creating additional grammar schools.
"Theresa May has embarked on a disastrous policy of re-introducing grammar schools without a shred of evidence that it will achieve her laudable aim to increase social mobility.
"The Government should listen to the evidence and ditch its intention to use 1950s' solutions to 21st century problems."
Malcolm Trobe, interim general secretary of the Association of School and College Leaders, said: "It is vital that Government policy is based on evidence rather than nostalgia and anecdote."
It added that the "misguided" policy was a "dangerous distraction" from the critical issues of a teacher-recruitment crisis and funding pressures.
A Department for Education spokesman said that it would ensure new selective schools prioritise the admission of pupils from lower income households or support other local pupils in non-selective schools to help raise standards.
"We know grammar schools provide a good education for disadvantaged pupils, helping to all but eliminate the attainment gap between disadvantaged pupils and their peers, and we want more pupils from lower income backgrounds to benefit from that.
"Our proposals are not about recreating the binary system of the past, which is what this report is based on.
"This is about creating more good schools in more areas, giving every child the opportunity to fulfil their potential, and we would urge everyone to look at the detail in the consultation and join that debate."