Faith schools are even more selective than grammar schools and do little for the poorest children in society, a report warns.
The Education Policy Institute's (EPI) research comes after Government plans to relax admission rules for faith schools.
Under new education proposals unveiled by Theresa May in September, faith schools will be allowed to select more pupils based on religion.
Current rules, which put a 50% cap on the proportion of pupils selected by faith, have been blamed for preventing new Catholic schools from opening.
The EPI's report found that pupils in primary faith schools "seem to do little or no better than in non-faith schools".
The report added: "Pupils in secondary schools record small average gains of just one-seventh of a grade higher in each of eight GCSE subjects.
"However, given that the average faith school admits fewer pupils from poor backgrounds than the average non-faith school, there is a risk that such small gains would come at the price of increased social segregation, with a risk of lower social mobility.
"If the objective of government policy is to increase social mobility, this policy intervention is unlikely to be effective."
Executive chairman David Laws, a former schools minister, said: "The Government has stated that it wants to create more good school places, and that this will help tackle the UK's social mobility problems.
"But Education Policy Institute research highlights the risk that expanding institutions such as faith schools and grammar schools will do little for the poorest children, and could even widen the social mobility gaps.
"While there are some faith schools which do admit a large number of disadvantaged pupils, our research shows that almost one in 10 secondary faith schools are even more selective than the average grammar school, and in general fewer poor children get admitted to faith schools."
Mary Bousted, general secretary of the Association of Teachers and Lecturers (ATL), said: "This Education Policy Institute (EPI) report is timely, adding crucial and up-to-the-minute evidence to the wealth of existing research which challenges the Government's politically-driven assertion that increasing the number of faith schools will increase social mobility.
"There are many excellent faith schools, as there are many excellent non-faith schools, and this evidence shows that it is pupil characteristics rather than a religious character that causes any difference between their outcomes.
"We know that evidence from research, and from the education workforce itself, is often unheeded by this Government, but surely these findings are too important and relevant for them to ignore.
British Humanist Association chief executive Andrew Copson said: "Allowing religious selection in admissions to state faith schools is often justified by lauding their academic performance.
"Today's report confirms that alleged academic superiority is a myth.
"It also demonstrates that Government aspirations to improve social mobility will be harmed, not helped, by their planned expansion of faith schools, which are in any case a disaster for religious segregation and community cohesion.
"The current cap on religious selection is popular and it has worked. We implore the Government to listen to the academic and public consensus and think again."