The last underground service, tomorrow night, from Hammersmith to Waterloo is at 11 minutes past midnight. (Change at Westminster).
Travel, within central London, on the Tube at night is very safe. (It's some of the outer London areas which can be a bit 'iffy'). When you travel during the afternoon you should travel at either end of the train (because these coaches are usually far less congested than the ones nearer to the middle). When you return in the evening, you might well find that you can have an entire carriage to yourself if you travel at the ends of the trains. Alternatively, if you board nearer to the middle, you'll have the added security of 'safety in numbers'. Just look around you and apply some good, old-fashioned common sense.
I've often travelled at night in central London, both by bus and by tube, and I've never had even the slightest worry.
You can plan your tube journey here:
http://journeyplanner.tfl.gov.uk/user/XSLT_TRIP_REQUEST2 ?language=en
Chris