A once-in-a-lifetime professional opportunity to work at the heart of government and contribute to our future with the EU”. This job ad for a senior policy adviser, with a salary of up to £70,302 and the ability to work flexibly, is for the Department for Exiting the EU (DExEU). We know the civil service needs new staff – it is hiring at least 15,000 recruits to cope with whatever lies ahead in the UK’s relationship with Europe. More interesting is that the job was posted on Mumsnet. It’s a sign that some parts of the civil service are finally starting to think more innovatively about how to tackle its widening gender pay gap.

It’s no coincidence that DExEU, a new civil service department created in July 2016 after the Brexit referendum, has been more agile in addressing the gender pay gap, including leadership programmes for female staff. Clare Moriarty, its new permanent secretary, is one of just five women departmental bosses in Whitehall, out of a total of 16.

Yet latest figures from December 2018 showed not only that the gender pay gap had widened at nearly a third of government departments over the previous 12 months, but also that staff who receive an internal promotion face a pay trap because of a cap on internal pay rises. While the cap applies to men and women, it affects more women, as men are more likely to leave the service for higher-paid jobs elsewhere, and then return on higher salaries. The Department for Culture, Media and Sport is one offender, with men hired externally at director level paid higher salaries than new female directors, all internally promoted and limited by civil service policy on internal pay increases. As a result, its median pay gap nearly trebled to 22.9%.

Despite commitments by Rupert McNeil, the civil service’s chief people officer, to address lack of diversity through “clear career progression and high-quality training”, the civil service is still failing to get round these pay differentials that still dog women, at all levels. But it’s not just about pay. Departmental culture differs hugely. It’s noticeable that the heads of the four biggest departments – work and pensions, justice, defence and HM Revenue and Customs – are all men. The Home Office and defence have a long-hours culture, whereas others like education tend to be more amenable to flexible working arrangements. Whitehall insiders also advise women aiming for senior posts to get as high as possible before having children, especially in private office work, which involves long days working closely with ministers.

Departments need to ask themselves some hard questions about how to unlearn some of these entrenched habits. Many are already doing so, including the MoD, where only 28.4% of senior civil servants are women, but where senior staff are making efforts to encourage women into defence jobs, as well as wider science, technology, engineering and maths roles, through outreach activities at schools and STEM events.

In December, McNeil wrote that the service “can and should be a leader for social change, in this case, in moving towards equality in pay”.

But the gender pay gap is not just a problem in the UK. Last month, European lawmakers in Strasbourg adopted an action plan calling for more women to be nominated for high-ranking and influential EU positions. On the same day, the feminist news site Newmavens reported that three men had been appointed to top-level banking and economic jobs at the European Central Bank, the Single Resolution Board and European Banking Authority. Well done, chaps.

Back at DExEU, despite its efforts to cast its recruitment net wider, its gender pay gap has actually got worse: increasing from 8.9% in 2017 to 14.5% in 2018. The reason for this jump is that women are joining the department at more junior levels, with more men coming into senior roles. For that to change, Moriarty will need to take much more drastic action, and more quickly.

Jane Dudman is the Guardian’s public leadership editor