He will be meeting with successful business women from across a range of sectors and will receive the Women on Boards six month progress report from Lord Davies and his steering panel.
Cameron is expected to make clear that although this progress is good news, and many companies have responded well to Lord Davies' call to action, he wants more businesses to step up and drive this forward.
The Government will also commit to publishing online a list of the number of women on the boards of top UK companies together with companies' pledges, in line with Lord Davies' recommendations. This is included in the Women on Boards six month progress report, as produced by Cranfield School of Management.
Women attending the event include Helena Morrissey, Founder of the 30% Club and Peninah Thomson of the Mentoring Foundation.
In February, Lord Davies published his recommendations on Women on Boards -
The latest findings published this morning show women make up 14.2% of FTSE 100 directors - up from 12.5% in 2010, women make up 8.9% of FTSE 250 directors - up from 7.8% in 2010 and 22.5% of all FTSE 100 and 18% of all FTSE 250 board appointments since publication have been female
There are 14 all male boards within the FTSE 100 - down from 21 in 2010 and 47.6% of FTSE 250 companies have all male boards - down from 52.4% in 2010.
Thirty three of FTSE 100 companies have set targets for the percentage of women on boards, however the majority of these companies already have fairly good representation of women on their boards.
Only 17 FTSE 250 announced board targets, again these companies were the ones already "doing well".
The prime minister is writing to all the FTSE 350 companies that haven't responded to Lord Davies' Women on Boards recommendations
In his letter the PM is expected to say: "Earlier this year Lord Davies published his strategy to increase the number of women on the boards of listed companies in the UK.
"Six months on, some important steps forward have been made: executive search firms have come together to form a voluntary code, encouraging the compilation of diverse candidate lists for the top jobs.
"Organisations like the 30% club are working hard to raise the profile of this issue. Progress is being made, but there is still a long way to go to encourage the best to rise to the top of industry, regardless of their background or gender. I am not proposing regulation or quotas - as coercion can undermine the real talent that is out there - but we do need more companies like yours to set out an aspiration to diversify your boards.
"Lord Davies' call to action was for all FTSE 350 companies to set out the percentage of women they aspire to have on their boards in 2013 and 2015 by September this year. As I understand, your company has not yet responded to this. I am therefore writing to you to ask you to do so. We will imminently be publishing all aspirations online, and I hope that we can look forward to include your company as part of that."
On 14 September Government (Home secretary, Theresa May), with BT, Tesco, Eversheds and the CBI, launched a new initiative to encourage business to publish gender equality measures as part of their reporting. "Think, Act, Report" asks private and voluntary sector employers to help tackle the pay gap through greater transparency on pay and other issues.
Women make up 51% of the UK population, 46% of employed people. Over the last 25 years the number of women in employment in the UK has increased by nearly a third, a total today of just over 12.5 million women.
The Women and Work Commission estimates that removing barriers to women working in occupations traditionally done by men, and increasing women's participation in the labour market, could be worth between £15 billion and £23 billion or 1.3% to 2.0% of GDP.
Based on current trends, it will take over 70 years for women to hold half of FTSE 100 corporate directorships.
Chris Parke, CEO Of Talking Talent, said:“It is, encouraging to see that David Cameron will be effectively naming and shaming those companies who have – so far – failed to make any impact.
“I am not in favour of quotas as a way of recruiting talent, but I do believe that action needs to be taken if we are to see more women operating at senior levels within business. The time has come for companies to promote the boardroom, and the benefits which go with it – they need to become attractive places for women to work.
“Companies need to focus on being more progressive when it comes to supporting women during pivotal points in their career, for example pregnancy and maternity. Careful analysis and management will work towards attracting and retaining core talent.”