I travel a lot late at night on the Central and Bakerloo lines, and I have never encountered any problems or anything that'd make me feel unsafe, and I'm usually very conscious of my safety, I won't even go to the shop on my own after 9 in my area!
I'd say that the next safest mode of transport will be a licensed mini cab, or a bus only if there isn't much walking involved to and from the stops.
I was waiting for my train at Harrow & Wealdstone not so long ago, and someone committed suicide on the track at the station so everyone was evacuated, the station was closed and the Bakerloo was suspended, so my only option was to try and figure out what bus to get.. So I got www.tfl.gov.uk up on my phone and used the journey planner to recalculate my journey, in the safest and quickest way. I recommend using it if you do happen to come across any problem. :)