The Investment Association (IA) has written to nearly a fifth of FTSE 350 firms asking them to explain how they intend to improve the gender diversity of their boards, which continues to lag the Hampton-Alexander Review's target of 33% representation of women by 2020.
It comes amid growing success in the pursuit for greater board diversity, with one-third of all FTSE 100 board positions now held by women.
However, according to the IA, more needs to be done, with 24 so-called "one and done" firms in the FTSE 250 that have just one woman on the board.
The 63 FTSE 350 companies the IA has written to include 13 that have been urged to take "robust action to address the lack of women in their top teams for a second year running", the trade body said, adding that asset managers "will be keeping up the pressure on companies during the 2020 AGM season to improve their gender diversity".
CEO of the IA Chris Cummings said: "We have seen steady progress with a growing number of women on boards. This is a critical year in which businesses need to demonstrate real change and meet the 33% target for gender diversity across their board and senior leadership teams.
"Diversity results in better decision-making and plays an essential role in a company's long-term success. Investment managers have been clear that as a minimum they want to see companies meet this target for gender diversity, and those which fail to do so risk facing dissent in the AGM season."
Philip Hampton, chair of the Hampton-Alexander Review, added: "Expectations from government and investors regarding gender balance at the top of FTSE companies, and in wider business have been clearly set out.
"The vast majority of companies understand the business benefits, have taken robust action in response and been working hard to improve the representation of women in leadership for many years.
"Leaders of FTSE 350 companies that are still adrift of the 33% minimum target, need to rise to today's challenge from the investment community and take swift action now to address the lack of women on the board and in their leadership teams."