The Christian charity has a contract from the government to offer support to victims who had been sexually exploited, subject to forced labour and held in domestic servitude.
More than 1,800 people were given support between April 2015 and March 2016 - up from 378 between July 2011 and June 2012.
In the past five years, the group has helped nearly 4,500 modern slaves, but Home Office figures estimate there are still between 10,000 and 13,000 slaves in the UK.
Almost half had been sexually exploited, 42% had been subject to forced labour and 13% had been held in domestic servitude, the charity said.
Sixty-two percent were women and 38% were male, with six transgender people supported.
The highest number of referrals were Albanian, with large numbers from Poland, Nigeria and Vietnam, as well as a "significant proportion" of British citizens. Almost one third of victims were trafficked to London.
Since its first year of running the government "victim care" contract in 2011, the Salvation Army has reported a year-on-year rise in the number of modern slaves being identified.
Major Anne Read, director of anti-trafficking and modern slavery for the Salvation Army, said: "Perpetrators go to great lengths to hide their crimes so it is always difficult to know the full extent of the problem. It may be that the increases in the numbers of people being supported is because there are more victims.
"The greater the awareness of this issue the more difficult it will become for traffickers to ply their evil trade in human beings."
