There is no single form of transport which is safe; the safety is relative to many factors.

When considering an issue which lingers in the minds of most females, or people who feel responsible over their female acquaintances or relatives, the biggest fear is of rape and of course the possible consequences.
If this is the only issue in mind, who do you entrust yourself or your loved one to? On top of the list especially at night time would be a black cab or through a licensed minicab office. If booked strictly in accordance to the law, the second option would be the most desirable one, and possibly the safest.
Following media coverage on this topic, especially that recently involving the serial black cab rapist, one is left with a number of unanswered questions.
Personally I would think that a service offered by somebody who apart from complying with the law has self respect, and respect for others. Anything else short of self respect, respect for others and the law would be self deception.
As there is no way of knowing who has these qualities apart from the legal requirement, the safest thing to do is to possibly be sober enough when using transport outside that provided by people known to you. Ensure you remain alert through out the journey, and if uneasy, end your journey when safe to do so, pay pro rata or if possible full amount, and call somebody known to you to come and pick you up. Always trust your instincts than live to regret.