0001 at Euston *from* Wolverhampton. The last Virgin / Avanti departure from Euston has been 2330 for some time.
I don't think there are any particularly symbolic 'midnight' departures across the network that go specifically at 2359 or 0001 for the reason of being a 'midnight train'. They are just as likely to be 2350, 2355, 2358, 0002, 0005 etc. For example the lowland sleeper leaves Euston at 2350 and Edinburgh / Glasgow at 2340. Euston has a departure to Watford at 2358 and Milton Keynes at 0002. Victoria has the last Brighton (Worthing) train at 0002, then final Southern departures at 0008 for Gatwick and 0013 for East Croydon.