It promises to be the hottest party in town; a huge Trafalgar Square bash to celebrate the end of the gender pay gap.

But there is just one catch. Guests have been asked to save the date – in 2235, the year that the World Economic Forum has said the gap will be closed, given the current rate of change.

Labour MP Stella Creasy said the party, which she has organised and which will be hosted by the mayor of London Sadiq Khan, carries a serious message.

“Shedding a light on a problem doesn’t necessarily do anything about it,” she said. “The government doesn’t have an explicit commitment to act on the causes of this gap and we want to change that. Enough talking about the pay gap – it’s time to take action to end it.”

The invitations went out as research carried out to mark Equal Pay Day on Saturday revealed that new gender pay gap reporting rules had not removed inequalities in the workplace. Equal Pay Day marks the day of the year on which the average female worker stops getting paid as a result of the gender pay gap.

Creasy called on the government to reinstall the explicit duty to act on pay inequalities into the public sector, which is only required to have “due regard” to the need to promote equality.

Marking Equal Pay Day, The Fawcett Society announced it was launching a legal advice service for women on low incomes to fight pay discrimination. The campaign is in partnership with employment law charity YESS Law and supported by a donation from former BBC correspondent Carrie Gracie.

It also revealed research which shows that frank discussions about pay are still rare, with six out of ten (61%) workers saying they would be uncomfortable asking a colleague how much they earn, while 52% said their managers would respond negatively to more transparency. One in three workers questioned by researchers did not know that it is illegal to pay women and men differently for equal work.

“Pay discrimination is able to thrive and is more common than people realise because of a culture of pay secrecy which persists,” said Fawcett chief executive Sam Smethers. “People do not know their basic rights and do not know what their colleagues earn.”

Research by the Young Women’s Trust to mark the day found that one in five young women said they had been illegally paid less than a male colleague for the same or similar work but less than half were confident they could challenge their employer about the gender pay gap. According to the charity, one in 10 human resources decisionmakers in organisations with more than 250 staff is aware of women in their organisation being paid less than men for jobs at the same level.

“Young Women’s Trust research shows that young women apprentices earn eight per cent less than their male counterparts, leaving them more than £1,000 a year worse off,” said the trust’s chief executive, Dr Carole Easton. “The sectors women tend to work in – such as administration, health and social care and retail – are not valued and paid as much as they should be.”

One of the factors driving the UK’s gender pay gap is that women are more likely to be in low-paid jobs and sectors, said Tess Lanning, director of the Living Wage Foundation.

According to Office for National Statistics figures, 3.8 million, or 28%, of all employee jobs done by women are paid below the real Living Wage, compared to 18% for men. The starkest difference is in the East Midlands, where 34% of women are paid below the Living Wage compared to 20% of men.

“Millions of women are trapped in jobs paying below a real Living Wage, particularly in administrative, cleaning and caring roles,” said Lanning. “Plans to improve gender equality must involve more businesses committing to pay a real Living Wage, not just the government minimum.”

On Friday the Women’s Equality Party encouraged working women to send Out of Office messages to mark Equal Pay Day.

“Women are rightly fed up at the lack of progress”,” said Catherine Mayer, president of the Women’s Equality Party. “Requiring companies to publish data on their gender pay gap is a waste of time if they don’t take action to close it.”

There were some glimmers of optimism, however. A small sample study from law firm GQ Littler, found that 39% of businesses have revised their hiring procedures in an attempt to close the gender pay gap, while 26% had conducted pay audits and 21% had changed pay policy. A survey for Totaljobs found that 46% of organisations who are taking steps to reduce the gender pay gap are actively promoting women into senior roles.

Earlier this month the Office for National Statistics revealed that the overall gender pay gap has fallen by half a per cent from 18.4% to 17.9% and the full-time pay gap has decreased from 9.1% in 2017 to 8.6% in April 2018.