There was a newspaper train that ran at about 3am from from London Bridge (Terminus) to Hastings until late 1987 or 1988.
Waterloo had passenger trains with newspaper vans (so not newspaper train) at about 1 or 2am, one went to Bournemouth, the other to Yeovil Junction (might have got destination wrong, but somewhere on that line), think they finished around same year, they were last mixed trains from Waterloo.
The last regular electric loco train with hauled stock from Waterloo was the Weymouth Boat train, which I think finished at end of summer 1987. (73s were used during the 4REP component recovery 1987-89, but they were with TC sets, not complete trains of hauled stock.