As New Labour's first education secretary, David Blunkett said he wanted to bottle faith schools' "ethos and success" and ministers have continued promoting them.
Since Labour came to power, 103 out of 112 applications to open faith schools have been successful, while religious groups have been encouraged to sponsor and run academies.
But the London School of Economics study said: "The fact that we observe higher attainment in the faith sector is no indication of the advantages offered by transferring a typical secular state school pupil into the faith sector because pupils currently attending faith schools are not typical.
"Pupils studying at religiously affiliated schools differ from secular students along several dimensions, many of which - such as family background - are correlated with their academic achievement."
The academics also blamed covert selection by schools.
The study used a Government database containing detailed information on around one million pupils attending more than 14,000 primaries to compare the key stage 2 test results of faith and secular schools.
After removing other possible factors, such as pupils' prior attainment and family background, their analysis found that in the average faith school an extra 1 per cent of 11 year-olds achieved level 4 or above in national tests compared with secular schools.
But David Whittington, Church of England acting chief education officer, said the research was "seriously flawed." He said: "Half of Church of England schools simply admit local pupils and most of the others admit a high percentage of local children."
'Faith primary schools: Better schools or better pupils?' was written by Stephen Gibbons and Olmo Silva, of the London School of Economics.