More than a third of partners at major UK firms went to a private school, compared to just 7% of the general population, a report by the Solicitors Regulation Authority (SRA) has found.

The report, published yesterday (17 May), reveals that 37% of partners in firms with more than 50 partners went to fee-paying schools.

Even in smaller firms, privately educated people make up 23% of partners.

The survey found that across the profession as a whole, 22% of lawyers went to private school.

The report concludes that law firms still have a way to go in improving the diversity of their staff.

Chief executive of the SRA Paul Philip said: "Encouraging diversity in legal services is not about ticking boxes. It is of course the right thing to do but it also helps to make sure the sector is as competitive as possible.

"There should not be any barriers stopping the best people – whatever their background – thriving in law."

The report is the third survey by the SRA on diversity in the profession. It surveyed more than 9,000 law firms in England and Wales and 170,000 people working in them.

It states: "Although the legal sector is increasingly diverse, more still needs to be done."

The survey also looked at gender, sexual orientation, ethnicity and social background.

It found that women make up 47% of lawyers across the profession, but that they make up just 33% of partners.

This represents an increase of two percentage points since the SRA's previous diversity survey, which took place in 2014 and found 31% of partners were women.

Meanwhile, just 14% of partners surveyed by the SRA identified as black, Asian and minority ethnic (BAME).

BAME people are still underrepresented in the profession, where they make up just 2% of lawyers – compared to 3% of the working population.

In 2011, a number of elite firms including Allen & Overy and Hogan Lovells founded PRIME, the diversity initiative designed to provide work experience in the legal profession to schoolchildren from less privileged backgrounds.

Earlier this year, a report by the National Foundation for Educational Research ran an assessment of the initiative and found that two thirds of the students surveyed – who had all undergone work experience placements at law firms – said they had not had any further contact with the firms since their work experience had ended.

The report recommends that firms now need to consider "manageable and effective" ways of maintaining this contact with students following their work experience.