London is the worst place to live in the UK if you're a woman, according to a report that reveals that women are less likely to work, earn less than men when they do, and are more likely to be sexually assaulted in the capital than anywhere else.

Ceri Goddard, chief executive of Fawcett, which produced the research using official figures, said: "This report is a really damning picture of where we have got to in London on gender equality. Our analysis suggests the gap between women and men in London is set to widen."

With unemployment rising faster among women than men and cuts to benefits that more women depend on – such as working tax credits – Fawcett and other anti-poverty campaigners expect more women to fall below the poverty line. The in-depth research, which offers a snapshot of London using figures from the Office for National Statistics and the Daycare Trust, suggests that women are more likely to live in poverty in London – with the rate as high as 4 in 10 women from black or other ethnic minority groups.

Sexual violence is also higher than anywhere else with 132 sexual offences for every 100,000 people in London according to figures from the ONS.

Despite warnings from rights campaigners that the situation in the capital is set to get worse over the coming years, Boris Johnson, the conservative candidate and favourite to win the mayoral elections on 3 May, has snubbed an opportunity to attend pre-election hustings on Monday called What About Women?Although it is a non-political society, Goddard said she was "extremely disappointed" in the incumbent mayor's decision to send a representative when other candidates had pledged to come and discuss the issue publicly. "I sincerely hope this is not an indication of how seriously he [Johnson] treats women's inequality," she said. "We've had enough platitudes. All the candidates need to be much more explicit about what their policies are doing for women."

A spokesman for Johnson said the mayor's decision was due to an "unfortunate clash of diaries".

The fact that many more men work in high-paid jobs in the City partly explains the far bigger pay gap in the capital, where women earn on average almost 22.8% less than men, compared with a gap of 14.9% for the country as a whole for full-time work excluding overtime. With 62% of all jobs and the vast majority of the highest paid ones held by men, the figures help skew the average. However, the relative paucity of public sector jobs as a percentage of the whole compared with other parts of the UK is also an important factor. The public sector has a far better record at employing women in higher paid jobs and offering greater flexibility, which is reflected in the fact that women earn 13.2% less than men on average in the public sector compared with 20.4% less in private employment.

High earners have a marginal impact on the fact that fewer mothers with dependent children work in London compared with elsewhere — just over half of mothers work in the capital compared with almost two-thirds across the UK. But the biggest single factor is the high number of lone parents. In 2009, 31% of families in the capital were lone parent families, and in most cases the parent was a woman.

A combination of the relatively high cost of childcare (up to a third higher than the national average), the distances travelled and the difficulty of finding flexible jobs all appear to be deterring a large number of women from working.

Fawcett has joined anti-poverty campaigners and the Institute of Fiscal Studies in expressing concern that changes to benefits will disproportionately hurt single parent households, who tend to find it hardest to work outside the home. Fawcett has warned that single mothers are set to lose 8.5% of their net annual income by 2015 — more than a month's income for every year — because of the impact of tax and benefit changes set to take place between 2010 and 2015. Cuts to the childcare element of the working tax credit introduced by the coalition government in 2010 is one of the most harmful changes.

Despite all this, the latest opinion polls from YouGov and the Evening Standard show that more women than men support Johnson. Goddard took issue with what she called some "stereotypical reporting that the women supporting Boris simply like a charming cad" and blamed the media's lack of interest "in proper policy debates".

The non-partisan Fawcett has launched a petition to raise awareness of inequality in the capital and asked all mayoral candidates to sign a pledge before the election which reads: "If elected as mayor, I pledge to assess the impact of all my policies, including spending decisions, on women and men, in order to demonstrate my commitment to closing the gap between men and women in the capital."

Val Pearman, who was made redundant after more than 30 years working in the British Library, explained the difficulty of getting another job. "When I was looking around to see what I could do if they turfed me out of the library, no one was offering any kind of paid employment – you know, it was like 'Oh we're not recruiting, but if you want to volunteer'. And this is in London. It's a real eye opener. It's not a good time, it's not a good time at all."