"This is tremendously disturbing," Radha Stirling, the group's founder and director, said in a statement. "Police regularly fail to differentiate between consensual intercourse and violent rape.
"Victims go to them expecting justice, and end up being prosecuted. They not only invalidate their (victimization); they actually punish them for it."
A UK Foreign Office spokeswoman said she could not discuss specific details, saying: "We are supporting a British woman in relation to this case and will remain in contact with her family."
It is understood that the Foreign Office is also in contact with two other British nationals.
The press office for the British Consulate in Dubai said it was supporting a British woman and her family, adding: "We have raised the case with the UAE Government, and would like to see it progress as quickly as possible."
Dubai is one of seven emirates that make up the United Arab Emirates, or UAE.
According to Detained in Dubai, the woman was "gang-raped" by the British nationals.
Stirling said the woman had been released on bail but had had her passport confiscated.
If convicted of consensual sex, the woman faces anywhere from a month to three years behind bars, followed by deportation, according to Faisal Alzarooni, a criminal defense lawyer who represents clients who've been charged with both rape and consensual sex in Dubai.
"The police or prosecution may have traces, but not necessarily evidence, that it was consensual sex. For example, if the rape was in a hotel room, if they saw on CCTV cameras that they (the accuser and the alleged attackers) walked together out of the room, they might think this is not rape in this case," Alzarooni said.
The Government of Dubai Media Office told CNN on Saturday it had no comment on the case.
A spokesman for Dubai police said he was unable to comment because the case was before the courts.