The Investment Association (IA) and the Hampton-Alexander Review have written to 69 companies in the FTSE 350 with no women or just one woman on their board requesting them to outline their action plans on making progress in gender diversity.
The letter reiterates companies must meet the Hampton-Alexander targets of 33% of women on their board and leadership team by 2020.
In February, the Institutional Voting Information Service (IVIS), the IA's voter information service, will give a 'red-top' - its highest warning level - to so-called 'one-and-done' companies who have just a single woman on their board.
Chief executive of the Investment Association Chris Cummings issued a call to arms for companies to do more than "take the tokenistic step of appointing just one woman to their board and consider that job done".
He commented: "Investors have been consistently clear they want to see greater diversity in the boardroom so it is totally unacceptable that one in five of the UK's biggest companies are falling so far short.
"There is also compelling evidence that boards with greater gender balance outperform their less diverse peers. These companies must up their game and explain clearly how they are planning to meet the Hampton-Alexander targets, or risk investor dissent at their AGM."
Sir Philip Hampton, chair of the Hampton-Alexander Review, said boards with just one woman "does not reflect the population of very talented women capable of making great contributions in boardrooms," while Rachel Reeves MP, chair of the Business, Energy and Industrial Strategy (BEIS) Select Committee, added that "old-fashioned attitudes to the role of women in the workplace still linger in some of the boardrooms of our biggest companies".
"The low numbers of women in executive positions can only hinder progress: gender pay gaps are highest in sectors with some of the lowest numbers of women executives.
"The time for our biggest companies to remedy the lack of gender diversity is long overdue and they need to set out what actions they are taking to make progress. The role of investors is important here too and they need to assert themselves to ensure that diversity is reflected more visibly at board level."