I think that there's scope for running trains past midnight on Mondays to Thursdays as well since people will often go to cinema, theatre, or even go clubbing (from what I've noticed it's only students who go clubbing on a weekday though!), and shift-workers, like people working in supermarkets, restaurants and in bars will need to return home too. Without a car, getting home after finishing work after the last train or bus has left can be very difficult if your place of work is not within walking distance of your home.
For instance, there should definitely be later services on the Cross City Line - I think at the moment the last service from Birmingham New Street to Litchfield is at about 23:15. Similarly, the last service from Southampton to Salisbury is at 23:38 Monday to Saturday - too early if you're seeing a show or going to a gig.
I also agree with SS4's idea that there should be more sleeper services, although I'd suggest couchette coaches should be used since they would be more affordable to leisure travellers. It would be fantastic if there was a sleeper service on the SW-NE/NW axis, or even a sleeper service from Bournemouth to destinations beyond Birmingham, but since most of the Mk3 sleepers have been scrapped or given to preserved railways it would be difficult to start such services. Converting a Mk2 or a Mk3 to a couchette coach should be easy, and there are surplus Mk3s courtesy of the collapse of Cargo-D, but unless the franchising system is reformed I can't imagine any TOC willing to take the risk, especially as running a sleeper service would have higher capital costs.