Cable is seeking put more pressure on companies to include more women on their boards, warning them "doing nothing is not an option".
The letter comes on the back of the announcement by gold mining firm Randgold Resources that Jeanine Mabunda Lioko has joined its board as a non-executive director. ??Cable has asked the remaining companies, Antofagasta, Croda, Glencore, Xstrata, Kazakhmys, Melrose and Vedanta, to explain what steps they have taken to increase their female board representation and how they plan to make their boardrooms more diverse.
According to the department for business, innovation and skills (BIS), the number of all-male FTSE 100 boards has fallen to seven from 21 in 2010.
Cable wrote: "My vision by 2015 is that Britain will not have a single FTSE 100 board without a significant female presence.
"This is not about equality, this is about good governance and good business.
"The international evidence supports this - diverse boards are better boards benefiting from fresh perspectives, opinions and new ideas which ultimately serve the company's long-term interests," he added.
The European Commission has proposed making it mandatory for companies to have 40% female directors on their boards, but the UK is among EU nations opposed to the idea.
France, Spain, Italy, Iceland and Belgium have introduced quota laws of their own.
In the letter Cable also wrote: "I do recognise that for some businesses, like those in the mining and extractives industry in particular, there are unique challenges in diversifying their boards with the right experience.
"The frequent travel and project-based work in remote areas of the world have all been cited as barriers to appointing more women in the past. However, successful modern companies learn to adapt and survive, and doing nothing is not an option anymore.
"We've seen examples again today that this can be done and I am determined to see further action."
Jill Rubery, professor of comparative employment systems at Manchester business school, told HR magazine: "My take on this is that it is a good idea to have quite significant quotas in order to extend the range of people and therefore the range of perspectives and opinions represented on boards currently.
"We can all see the problems with boardroom cultures particularly in the banking sector and the slow incremental approach favoured by Cable will have limited effect. It is less important to have, for example, one woman on each board- as Cable is in effect asking for in the men only mining and natural resources industries - than to have a sufficient representation to make a real change in culture in at least some companies and sectors.
"However, it is difficult to make this step change as women are also underrepresented in lower levels of management. Any immediate action needs to be combined with a policy of widening representation in general on boards to include employee representatives in a move towards more stakeholder capitalism."
