The party, founded by Catherine Mayer and Sandi Toksvig, is facing its first real test as Ms Walker goes head to head with 11 other candidates to win over the city's residents by May.
But what are the Women's Equality Party promising for London? Here are 14 things they pledge to change if the party is voted in:
1. Parties to join forces to solve London's housing crisis
A cross party committee examine the housing crisis and work together to tackle it, rather than one party.
2. Reducing childcare costs using the budget
Subsidised childcare costs to help mothers will be introduced so unemployment reduces and parents are able to regain the confidence and financial stability to get back to work .
3. Specific Night Tube officers patrolling trains
To protect people travelling and "make the city safer", the party wants to work with British Transport Police to ensure those on the Night Tube are protected.
4. Carriage-less trains will be made
Introduce carriage-less trains quicker so that people can move away from others when feeling threatened during commute.
5. Businesses to incorporate women's needs
Implementing business policies to incorporate women's needs, such as flexible working hours and more in-office creche facilities.
6. Name and shame companies with gender pay gap
Publishing the names of offending companies to examine how severe the gender pay gap issue is across the city, before eradicating it.
7. Create safe havens for women running from violence
Those suffering from domestic violence should be protected by establishing a London-wide register of accessible refuge spaces.
8. Join the battle against Heathrow expansion
Fight against the Heathrow Airport third runway proposals but agree to expand the city's infrastructure.
9. Helping more females get into STEM
Putting into place a Women's Enterprise Board which gets more women working in industries such as Science, Tech and Business.
10. Earlier careers advice and better services to get people into their chosen industry
Work with London schools, careers officers and initiatives such as CodeClub and Stemettes to address gender stereotyping in school and career choices to make sure career advisors encourage young people to pursue the careers they want.
11. Invest in a better cycling infrastructure
More cycling should incorporate what works for women and families, including more segregated cycle lanes, while consulting closely on the impact of new systems.
12. Make violence against women a priority to reduce
Build on the Pan-London strategy on Violence Against Women and Girls, in partnership with women’s organisations, and deliver a holistic approach to tackling violence against women and girls.
13. Train services to get a better understanding of cultural related violence
Work in partnership with specialist BME women’s services to ensure that Female Genital Mutilation (FGM), forced marriage and so-called honour based violence never happen in London.
14. Create a more diverse police force and train officers to understand violence against women
Met police officers to be trained in identifying a diverse range of issues surrounded women's violence