Who runs Britain? There are few meaningful opportunities for women, according to Monday's report on Sex and Power by Counting Women In, a coalition of five organisations including the Hansard Society and Unlock Democracy.

David Cameron says he wants more women around the cabinet table, and he could of course get on and appoint them. But the greater problem is the number in the room. The Commons still has the feel of a boys boarding school – just over 22% of MPs are women, and Britain continues to fall down the international league tables.

Allegations about the Liberal Democrats' "casting couch" are very serious, but the problem for those seeking selection for winnable seats goes far deeper than any risk of sexual harassment.

The electorate does not discriminate against women when presented with a choice, but those selecting candidates at local level still prefer men. I am often reminded by those who do not see the exclusion of women as a problem that "the cream rises to the top" but in politics so too does a fair amount of froth and hot air.

So far, Labour's all-women shortlists have been the most effective means to reduce the imbalance – but surely something is wrong when you have to force a small "selectorate" to choose a woman candidate? Labour's 33% women still doesn't feel like a great success, especially on those terms. Who wants to feel that they were the best woman and not the best candidate?

The Conservatives experimented with open primaries at the last election but local hustings events made little difference to the proportion of women selected. I was selected via the first all-postal open primary where every voter had the opportunity to select the candidate. Both such primaries returned a woman candidate – Caroline Dinenage is also an MP as a result. While that is too small for any statistical significance and too expensive to roll out at national level, it is a shame there have been no pilots of lower-cost options to engage more people in selections. In "safe seats", which never change party allegiance, candidate selections are in effect the election and it is worth continuing to explore ways to widen participation.

Countering male bias also requires more women to consider politics in the first place. All party leaders should be encouraging women from non-political backgrounds to apply. You don't need to have "done politics" to be an MP, but it should be a necessity to have seen a bit of the real world.

I often ask women why they don't think of applying. After all, for all the negativity, it is still one of the most interesting and demanding of roles. The impact on family life deters the most, and they are right to be concerned. But it doesn't have to be that way. We could learn from other professions that have embraced job sharing as a way to encourage and retain staff as they juggle family and career.

I job-shared for 11 years as a doctor before coming to parliament. It's a wonderful way to work and it makes for built-in mentoring. For MPs it would allow for complementary experience that would broaden their combined expertise.

Having worked in three different types of job share, the secret of success is a close ethical fit with your partner and a similar approach to work. As an MP, I could not job share with an anti-abortionist or a "hanger and flogger". I voted for same sex marriage, but what if my job-share partner felt equally strongly the other way? The answer is to make sure you have a similar ethical framework before you start, and to apply it as a pair. Where disagreements arise over policy issues then the vote goes with the manifesto commitment or majority constituency view. In some circumstances the agreement would have to be to abstain, but only one MP votes at any one time and they would share a single salary, staff support, office and London accommodation.Job sharing opens parliament to more people with disabilities and does not exclude men who want to take on caring roles as well as hold down a career in politics. Legal opinion is that job sharing is perfectly compatible with being an MP.

It is time to start looking at how it can be made to work. Ultimately, voters would decide. They may well take note of job sharers in other professions, who between them often deliver far more than a full-time equivalent.

To those who say it will never work, the question has to be: does the current system always work out so well? Having a single MP is no guarantee you won't get a dud.

To deliver a more equal government takes decisive action at every level, from encouraging applicants right through to Cameron's cabinet – but time is running out if the prime minister wishes to see this fixed in time for 2015.