The most popular state schools in England are increasingly demanding that pupils display a particular talent for music, science or sport in order to secure a place, according to new research.

A government crackdown on covert forms of selection has coincided with more and more high performing state schools, faith schools and academies giving priority to pupils with talent in the schools' specialist subject, academics at the London School of Economics have found.

The survey of admissions practices in 3,134 schools last year reveals how many use lotteries to allocate places: some 6% of schools now use a lottery as part of their admissions process.

An admissions code introduced two years ago has put a stop to most discriminatory methods of selecting pupils and has forced schools to prioritise children in care, it found. But a minority of schools continued to break the new rules, for instance, by asking questions about parental occupation and marital status. Some schools had replaced interviews, which were banned under the code, with "pre-admissions meetings," the study said.

The research reveals that 5% of schools now select some pupils according to aptitude – up from 3% in 2001. Schools are allowed to select up to one in 10 pupils by aptitude under the specialist schools programme. Some 15% of academies, 14% of foundation schools and 7% of faith schools selected according to aptitude compared with less than 1% of community schools.

The main charge against the admissions process is that it is still too complex for many families to understand – and faith schools were found to be the worst offenders. Professor Anne West, the lead researcher, said: "Despite improvements our research suggests that the system is still too complex, particularly for parents and carers who are not highly educated or proficient in English, and especially where there are schools responsible for their own admissions."

Sarah McCarthy-Fry, the schools minister responsible for admissions, said: "Admissions authorities must ensure their arrangements are not unnecessarily complex so as to disadvantage certain families. This is not acceptable practice and the adjudicator can use his newly-enhanced powers to investigate and correct where needed."