Mansa, a 33-year-old Ghanaian woman who days ago was close to being deported, has no doubt that the Poppy Project saved her life. "I was ready to kill myself if I had gone," she said. "I didn't know what else I would do."

Hundreds of other victims of sex trafficking in Britain may not be so lucky. Shortly after midday last Monday, an email confirmed that ministers were withdrawing funding from the charity, which pioneered specialist services for victims of sex trafficking, and is the biggest and most established organisation of its kind.

The government decision immediately prompted a campaign by luminaries such as Professor Liz Kelly, the chair of the End Violence Against Women Coalition, and urgent appeals for donations to help the project continue supporting victims of trafficking.

The withdrawal of funding means that the charity requires £450,000 in donations by the end of June to continue. The impact of the funding cut on trafficking victims – an issue that David Cameron says is a "key priority" – is potentially catastrophic, according to the organisation's case workers. Abigail Stepnitz, the national co-ordinator for the Poppy Project Eaves charity, said that the decision was "politically motivated".

"The government doesn't like someone who will rock the boat. We were a problem for them in that sense," she said. Since the charity joined an oversight board two years ago, assessing the government's compliance on tackling trafficking, it has successfully appealed 17 UK Border Agency decisions on identification of trafficking victims and forced countless reassessments.

Last week's decision has also crystallised concerns that the coalition government does not regard sex trafficking as a priority – regardless of Cameron's pledges. Stepnitz points to letters from officials, which concede that, while the rape experienced by victims is "unfortunate", it does not qualify them for government help.

Her all-female team of 16 support workers provides around-the-clock support and accommodation for those women who are trafficked to Britain and forced into prostitution or servitude. More than 700 have received help since the organisation was founded in 2003.

The organisation's virtues were underlined by the rescue of Mansa, days before news of the funding decision. In 2003, the Ghanaian had been taken from Heathrow airport to a rural house where she was held and "tortured and sexually abused" over four years.

Faced with her deportation, the Poppy Project argued that, after eight years in the UK and with an abusive family in Ghana, she would be better to receive continuing support at its Sheffield office. On the morning of her scheduled deportation flight from London on 1 April, Poppy staff acted to keep Mansa in the country. They contacted the pilots' union, explaining the situation. Leaflets were printed and distributed to passengers at Heathrow, and every legal avenue explored. Stepnitz made an application to the European Court of Human Rights. It paid off. Less than four hours before the flight's departure, the government backed down.

"Poppy saved me. They helped me emotionally, mentally and support every bit of my life. But without the funding it's going to be very tough. A woman who has been tortured, raped and beaten needs a lot of support to get better," she said.

Another of Poppy's success stories, Maria, 24, was trafficked from the Balkans to London by a neighbour when she was a child. Despite claiming asylum almost a decade ago, the government had never responded, leaving her unable to work legitimately and forcing her back into prostitution to survive.

At the start of 2011, a friend told Maria that help was available. "Before the Poppy Project, I had never felt like a human being, I was never treated as a human, I was always treated like a dog," she said. "For seven years I didn't live something I could call life. Now I feel free and happy, Poppy has given me power I never had. Now I want David Cameron to come here and talk to us, hear how we feel."

But the damage may have already been done. The £4m contract for services that the charity developed went instead to the Salvation Army, a decision that the government said was "much better for victims of trafficking".

One element of the decision that had troubled support workers was the assumption that most victims would require only 45 days of treatment. Stepnitz said that at least 90 days was required to rehabilitate victims. The average length of treatment at the charity, which can support 128 women, is between three and eight months.

Within the charity's south London headquarters are the tools of rehabilitation. Trafficked women learn English, how to write CVs, computer skills and how to eat healthily. Between shifts manning the emergency referral and advice hotline, Leigh Ivens and her colleagues escort women to see doctors, meet Home Office officials and solicitors. They may eventually escort them to court to testify against their trafficker. The charity has secured more than 500 years in convictions against traffickers.

"But really it is about getting women to the stage where they have their freedom back," said Ivens, who this week will adopt another role – campaigning to raise the £1.8m a year required to help women like Maria and Mansa.

Donations to the Poppy Project can be made via Eaves' website