Based on undergraduate admissions between 2004 and 2010, the Campaign for Science and Engineering (CaSE) found that only about 25 per cent of students entering physics or maths courses came from blue-collar backgrounds, compared with 30 per cent of all higher education students.
The demise of the triple science GCSE in state schools and a shortage of specialist maths and physics teachers working in deprived areas have contributed to the problem, the report says.
Students at state schools are also less likely than their private school peers to study science disciplines at A level, it adds.
The closure of science departments at some universities has also reduced the options for state pupils, who are more likely to study closer to home, it argues.
Imran Khan, director of CaSE, said it was vital to tackle the issue because science could be missing out on many bright students from poorer backgrounds.
Students who graduate in scientific subjects also earn 20 per cent more than those working in other fields, he added.
"It is not just an issue for universities," Mr Khan said. "It needs to be tackled much earlier in the school cycle when schools are considering their science provision. What is particularly worrying is that we have not seen any improvement in social diversity when, overall, diversity is increasing at universities."
He warned that the underlying factors causing the differences in maths and physics participation had not been addressed.
"Of those taking GCSEs and A levels, independent school pupils are still over-represented in science and maths subjects...Even for the cohort about to start their GCSEs, the underlying factors influencing their choices have not changed," Mr Khan said.
However, despite concerns over maths and physics, computing and biology courses have proved more popular with poorer students.
About 38 per cent of students on computing courses during the period assessed hailed from blue-collar backgrounds, while the biological sciences were marginally more popular among the working-class group than other subjects.
The proportion of state pupils and working-class students enrolling in engineering and technology was largely in line with all subjects, although there were fewer applications from pupils living in deprived neighbourhoods, according to the report.