At last in British politics there is some certainty; the country will be led by its second female prime minister and it is difficult not to be swayed by the unprecedented nature of the contest for the Tory leadership.

But there are many who are seeking to reach beyond the focus on gender and power and ask whether either of the two females on the shortlist to become the most powerful politician in the country will do anything for ordinary women.

The Fawcett Society, in a letter to Andrea Leadsom and Theresa May, to be published on Monday is calling for a commitment from both candidates that there will be no going back on women’s rights.

Sam Smethers, the chief executive of the Fawcett Society, said: “We want to get more women in positions of power and obviously 52% of the population needs to be better represented. But it is not good enough just to be a woman in power, you need to make life better for women outside in the real world. We want Andrea Leadsom and Theresa May to commit to improving the lives of women throughout the UK and in our letter we are calling for a progressive agenda not a backward-looking agenda.”

Key areas identified by the Fawcett Society include maternity rights, part-time workers’ rights and the gender pay gap. Here’s how the candidates stand:

Maternity rights

Leadsom: The junior energy minister, who worked in the City while bringing up three children, has called for women working in small businesses to be stripped of their right to maternity leave and unfair dismissal in a bonfire of workers’ rights to allow small businesses a chance to “get off the ground”. But in her leadership speech she talked of the “unfortunate prejudice faced by working mums” and promised to stand up for them.

May: The home secretary and former minister for women and equalities, voted to remain in the EU, where directives including the EU pregnant workers’ directive 1992 led to improvements in the health and safety protections for expectant and new mothers in the workplace.

Part-time workers’ rights

Leadsom: Has called for no regulation whatsoever relating to employment rights for full- and part-time employees to encourage small firms to grow. Women account for 75% of part-time workers.

May: Has spoken of the need to get women part-timers into full-time jobs, saying: “One way in which I’m particularly keen that our economy becomes fairer is in the opportunities available to women.” As a remainer, she wanted the UK to be part of an EU that gave women working part time in the UK equal access to occupational pension schemes, after a case in the European court of justice.

Childcare

Leadsom: Passionate about the the importance of the infant years and the need for children to have close attachments to their parents. A committed Christian, she said “the period from conception to age two” is key to achieving social justice and improving the emotional health of the nation. She is a prominent advocate of specialist services supporting women and babies and has spoken of transferring the budget for young offenders and crime prevention to provision for the under-twos.

May: Has spoken of the need to get women into work and exploit the huge untapped potential of the female workforce. “If we fully used the skills and qualifications of women who are currently out of work, it could deliver economic benefits of £15bn-21bn per year,” she said.

She supported the government’s decision in April 2015 to allow parents to take 18 weeks’ parental leave for children from the age of five to 18 – a right that came from an EU directive.

Violence against women

Leadsom: Has not spoken out on the issue.

May: Has made violence against women a key area during her time as home secretary, and won round many feminists and women’s groups with her continued commitment to tackling the issue. Under her leadership at the Home Office, the law of coercive control to tackle domestic violence was introduced and she set up a nationwide inquiry by the HMIC into how the police dealt with domestic violence. But on migrant women who, campaigners say, are subject to domestic violence, immigration control and no recourse to public funds, May is less outspoken. She defied a call to end the detention of pregnant women in Yarl’s Wood, saying they needed to be held for short periods to be quickly removed.