Dozens of companies, including Domino's Pizza, JD Sports and Greene King, have been told to put more women on their boards.
The Investment Association, a financial sector business entity and the government-sponsored Hampton-Alexander magazine wrote to 69 companies.
They asked them to have 33% of their boards set up by women by 2020.
The magazine has threatened to label them as "red tops" as a warning to investors about their lack of gender diversity.
They said that it is "unacceptable" that one in five of the UK's largest companies in the FTSE 350 index is not up to gender diversity.
Among the identified companies, 66 have a single woman on their board of directors, while three companies – Daejan Holdings, Millennium & Copthorne Hotels and TR Property Investment Trust – have a completely male board.
& # 39; unacceptable & # 39;
The Investment Association has 250 members who manage assets of 7.7 t £. His boss Chris Cummings has stated that it is "unacceptable" that one of the five largest British companies is not at the height of gender diversity.
"Companies need to do much more than take the tokenistic move to appoint a single woman to their council and consider that the job is over.
"There is also convincing evidence that councils with a greater gender balance outweigh their less diverse peers," he said.
The Hampton-Alexander magazine was commissioned by the government in 2016 to address corporate gender inequality and set goals for the largest British companies.
Sir Philip Hampton, who presides over the magazine, said that the fact that companies failed to bring women into the boardroom and take on management positions "does not reflect the population of highly talented women who can make great contributions on the boards of directors ".
Rachel Reeves' deputy chairman of the company selection committee said that the low number of women in management positions may hinder progress as gender gaps are higher in sectors with few women managers.
He said: "Here too, the role of investors is important and must assert themselves to ensure that diversity is reflected more prominently at board level".
Other companies on the list that have only one woman on their board include St James's Place, 888 Holdings, Just Group, Acacia Mining, Stobart, Restaurant Group and Softcat, among others.