The last few places I have worked, before I began working for myself, I was jointly responsible for setting salaries, conducting reviews, assigning responsibilities, recommending and in some cases approving promotions.
The corporate workplace (to my thinking) is a balance of competing interests. Employers do not want to pay out more than they have to, but by the same token they have no wish to lose undervalued staff. In key positions especially.
Good companies will base pay around a market rate, achievement, and if they are really sensible they will reward loyalty and commitment too.
Where I have worked, which has been within both major and minor corporations in the IT industry in project and account management, women achieve equal pay to men. And in very well paying jobs too.
I cannot dispute that pay disparity does exist, I am not sure how best to solve it. In highly skilled jobs, people by and large write their own payslips within market constraints with no regard to gender.
In lower paying jobs that are easy to resource, employers will pay as little as they can get away with. It is those positions where I believe women are at their most vulnerable. Unionization can help a lot. Educating employers can help a lot too. If workers feel that they are undervalued and discriminated against, their productivity drops, stress levels rise, turnover becomes an issue, they are more prone to sickness.
As far as lobbying goes - yes - enacting changes in law is a very positive step. One that has been taken in terms of equal opportunities and anti discrimination, yet those laws are hard to enforce because they are generally hard to prove. Still they are good steps.
The main ways I believe women can obtain parity are
1) Collective Bargaining
2) Educating Employers on the Benefits of Equal Pay
3) Cultural Acceptance of Equal Pay (within the corporation)
4) Assigning a Responsibility within Human Resources to Manage and Foster Diversity. Measure and Metric.
5) Enshrining Equal Opportunities and Anti Discrimination in Law, and Educating Employers to Ensure they Understand their Obligations.
Those 5 measures would go a long way to help fix things, in my opinion.