The Poppy Project, run by Eaves since 2003, has received £1.8m from the government for each of the past two years under a contract to provide specialist accommodation for female victims of trafficking.
But the Ministry of Justice has decided that the funding for the service for the next three years, which could total as much as £6m, will be awarded to the Salvation Army.
A spokeswoman for the Poppy Project said it would have to make 14 of its staff redundant at the end of June as a result. The charity has 70 staff and 15 volunteers.
Eaves' Poppy Project offers 54 bed spaces – 37 of which are in London, with the remainder divided between locations in Cardiff and Sheffield – for the victims of trafficking. This number will be reduced to 16 because of the withdrawal of funding.
The decision to award the contract to the Salvation Army has sparked controversy.
In a joint statement, Liz Kelly, co-chair of the End Violence Against Women Coalition, and Vivienne Hayes, chief executive of the Women's Resource Centre, said they were astonished that the Ministry of Justice had awarded "vital public funding to support victims of sex trafficking" to a religious group rather than a women's support service.
"There is a wealth of evidence to show that women who have experienced violence want a specialist service that understands their experiences and needs," the statement said.
"Moreover, women's organisations that have built up years of practice-based evidence supporting survivors and tackling abuse are more effective in enabling women to overcome the harms of abuse and rebuild their lives."
The statement also expressed concern about how the government would ensure that "evangelical religious organisations" would not discriminate against women and "make moral judgements about their situations and needs".
"How will the Salvation Army respond to lesbians or women who need abortion advice?" it asked.
The Salvation Army website says that the organisation believes, in cases of unwanted pregnancy, that it is best "for the foetus to be carried to term". It adds: "in cases of proven rape or legally defined incest, an abortion may be justified".
On homosexuality, the organisation's website says that "homosexual conduct is controllable and may be morally evaluated therefore in the light of scriptural teaching" as "the Bible teaches society should be ordered on the basis of heterosexual unions".
But Anne Read, the Salvation Army's anti-human trafficking response coordinator, said the organisation would offer "unconditional assistance and support regardless of race, religion, gender or sexuality".
A spokeswoman for the Ministry of Justice said bidders for the contract were required to demonstrate that they would ensure equality of access to support services for all victims, "regardless of their religion, gender, sexuality or ethnicity".