"Do not go out of the village wearing TeamGB kit or carry anything of value unless absolutely unavoidable - this makes you too big a target for theft/crime," it adds.
"You MUST inform a member of team management if you are leaving the village and planning on staying out overnight - please do this BEFORE you leave."
Athletes were ordered to attend a BOA security briefing upon the completion of their events. "This is absolutely essential - there are no excuses for not attending. If you can't make the morning after you finish, go the morning after that - this is for your own safety."
The warning continued: "Rio is NOT a safe environment, and the level of crime has spiked in the last few days," it adds.
"Think very carefully about whether it is worth the risk of leaving the village to celebrate after you have finished competing - BOA/UKA staff cannot guarantee your safety when away from the village/British School/British House. Our strong advice is that it is simply not worth the risk given the current climate in Rio."
Curfews have been imposed by other National Olympic Committees on their athletes due to a spate of muggings in Rio.
The BOA e-mail warned that "if further safety/security issues arise it is likely that an outright ban on leaving the village after dark will be introduced".