There are now just four FTSE 350 companies that have all-male boards, down from 152 in 2011. But there are another “40 or 50” companies which have just one woman on their board, Ms Wilson said, which the review is now applying pressure to. “At the beginning we worked very hard on all male boards,” Ms Wilson said. “We now have very few of those. The next stage is turning our attention to what we call ‘one and done’ firms, where they appointed one woman several years ago and are not for changing.” “What are the tools, what is the wherewithal they have to encourage – force if you like to use that word – these companies to use their entire talent pipeline and not just half of it?” she said.“If they choose to ignore that I do think there needs to be some way of addressing that actually.”The review, which will report to the Government at the end of next year, is to publish figures on Monday showing that 32.1 per cent of FTSE 100 board positions are held by women, up from 12.5 per cent in 2011. Over the same period, the FTSE 250’s figures have increased from 24.9 per cent to 27.5 per cent.Kelly Tolhurst, the business minister, said: “These latest figures show there are now more women than ever before at the top of UK business, and I want to see companies do all they can to increase the numbers further. “Diversity makes good business sense and those who fail to see this as a priority are missing out on the benefits that diverse leadership brings.” Since mid-March when the letters were sent, 20 have now appointed women but 14 failed to reply to the letter at all, according to figures published on Monday as part of the review’s mid-year update. Ms Wilson said the lack of response from 14 companies left her feeling “frustrated”.“There are a small number of companies that are holding things back – and the question is what do we do about them?” she said.A voluntary regime can be “persuasive”, she said, adding: “But we are powerless in terms of giving any sanction or doing anything about these companies that choose not to address the shortfall of women in their leadership team. And I think that is where going forward, is the next stage.”Ms Wilson said that while she would not advocate “quotas and legislation per se”, ministers must consider how to bring these reluctant companies to the table. The Hampton-Alexander review encourages all FTSE 350 companies to have women make up at least a third of their board and leadership roles by the end of 2020.Along with the Investment Association – which represents investors responsible for funds totalling £7.7trillion – the review wrote to 69 firms companies which had one or less women on their board. Some of the UK’s top firms are taking a “one and done” approach to gender diversity by appointing a token woman to their board, a Government-backed review has found. A small number of FTSE companies are “intentionally blocking progress”, according to Denise Wilson White, chief executive of the Hampton-Alexander review which was set up by Theresa May in 2016 to close the gender gap at the top of business.Ms White told The Telegraph that some businesses are “still keeping their hand in the sand” and “turning a blind eye” to their lack of female leaders.All big firms “know the right lines to say” when asked about gender diversity, she said, but despite the “warm words” and rhetoric, “many don’t get it at all”. Last year, the Telegraph launched its Women in Business campaign aimed at encouraging the development of policies designed to help female entrepreneurs. Want the best of The Telegraph direct to your email and WhatsApp? Sign up to our free twice-daily Front Page newsletter and new audio briefings.