Some of the UK's biggest firms are being urged to do more to recruit women into senior positions.
The call came in a government-backed review which found that FTSE 100 companies were "on course" to meet a voluntary 33% target for women on boards by 2020.
But it said smaller firms on the London Stock Exchange were lagging behind.
To hit the target FTSE 350 firms would need to fill at least 40% of top jobs with women over the next three years.
The report - the Hampton-Alexander Review 2017 - is a government commissioned review into increasing the number of women in senior business roles.
It found that in the FTSE 350, Royal Mail, Next, Severn Trent and Diageo had the most women in top jobs, while the Sports Direct, 888 Holdings, Just Group, Metro Bank and the London Stock Exchange were among the companies with the fewest.
When published its initial findings last year the review set voluntary targets of:
- Boards with 33% women in FTSE 350 firms by the end of 2020
- FTSE 350 companies to increase the number of women in the role of chair, senior independent director and executive director on their boards
- FTSE 100 executive committees to comprise 33% women, with the same figure reporting directly to the executive committee, by 2020
However, not much progress has been made in the 350 biggest firms listed in London, outside of the hundred biggest firms, said review chairman Sir Philip Hampton.
"This year we have seen progress pick up on FTSE 100 boards and go slow elsewhere," he said.
Sir Philip called on FTSE 350 companies to "quicken the pace of change on boards".
He also extended the voluntary target of 33% target of women in senior leadership positions below board level to all FTSE 350 companies. Previously it only applied to FTSE 100 firms.
Highest ranked FTSE 100 firms for women on boards and in leadership
2. Severn Trent
6. Merlin Entertainments
7. Old Mutual
9. Scottish Mortgage Investment Trust
10. Intercontinental Hotels Group
Institute of Directors chair, Lady Barbara Judge said the "next challenge" was to increase the proportion of women in senior executive positions.
"In this way, we can build a pipeline of female talent to consolidate and build on the improvements we have seen in the last few years," she added.
One solution would be to encourage more girls to do sciences and maths and to bring to an end the idea that there are 'girl jobs' and 'boy jobs'".
However, she said men also needed to "step up" in areas such as parental leave entitlements.
"Employers should encourage their male employees to take more parental responsibilities to allow women greater opportunities to get back into and on in work," she said.
Lowest ranked FTSE 100 firms for women on boards and in leadership
100. London Stock Exchange Group
99. Mediclinic International
94. Smurfit Kappa Group
92. Babcock International
91. International Consolidated Airlines Group
90. Paddy Power Betfair
Human resources trade body, the CIPD, said the Hampton-Alexander Review was right to "focus on increasing the gender balance of the management talent pipeline across the FTSE 350".
But, it added, more attention needed to be paid to executive directors at board level.
It said it had "consistently called" for an additional voluntary target for 20% of FTSE 350 board-level executive directors to be women by 2020.
"It is the impact of visible female role models in executive director positions that has the most potential to change organisational culture and practices around gender diversity and encourage more senior level progression for women directly below board level," it said.
Hampton-Alexander Review 2017
- 27.7% of board positions in FTSE 100 companies were held by women in 2017; in 2016 it was 26.6% last year; in 2011 it was 12.5%
- 22.8% of board positions in FTSE 250 companies held by women in 2017; in 2016 it was 21.1%; in 2011 it was 7.8%
- 24.5% of board positions in FTSE 350 companies held by women in 2017; in 2016 it was 24.5% in 2016; in 2011 it was 9.5%