The alliance has also
launched a petition for the new legislation, which would see employers become legally liable if they fail to protect their staff from sexual misconduct.
The duty on organisations would be supported by a code of practice, including mandatory training for staff and managers, and clear policies.
The alliance, This is Not Working, is backed by 28 organisations, including Amnesty International, Business in the Community, Fawcett Society and Time's Up UK.
Fawcett's chief executive Sam Smethers said: "We need to strengthen the law to better protect women from harassment from co-workers, clients or customers and we need a new duty on employers to prevent sexual harassment. They have to take responsibility for their own workplace culture.
"Everyone is entitled to dignity and respect at work. Sexual harassment has no place in any workplace."
In May, the government said it would launch a consultation on workplace sexual harassment "shortly". This will consider evidence for introducing a new duty of employers to prevent harassment and extending the protections of the Equality Act to volunteers and interns.
Under current law, it is the victim's responsibility to report sexual harassment at work to their employer after it has happened.
The petition says: "Our laws rely on individuals reporting but #ThisIsNotWorking. The onus is on the victim to report -- which can be isolating, confusing and potentially traumatic. Four out of five don't feel able to report sexual harassment to their employer.
"It should not be down to the individual to prevent and manage their harassment alone.
Research by the TUC found that more than half (52%) of women have experienced sexual harassment at work. However, 79% of these said they did not feel comfortable reporting it to their employer, suggesting that "harassment continues unchecked in workplaces across the UK", the TUC said.
Its general secretary, Frances O'Grady, said: "It's shocking that in 2019 so many people experience sexual harassment and assault while at work.
"The government must strengthen the law to put responsibility for preventing harassment on employers.
"This would shift the burden of tackling sexual harassment away from individuals. And it would help end toxic workplace cultures that silence those who've been harassed.
"We're calling on everyone who wants to stop sexual harassment at work to join us and call on minister to take action."
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