For example, I believe that there was a limited overnight service on the Kingston Loop until about the mid 1980s (probably killed off by the move of a lot of newspapers away from Fleet Street) and a number of overnight newspaper trains from Waterloo (and indeed on many other routes throughout the country).
From winter 1972 Southern Region public timetable -
0130 and 0348 Waterloo - Wimbledon - Kingston - Twickenham - Waterloo (arr 0244 and 0502)
0135 and 0325 Waterloo - Twickenham - Kingston - Wimbledon - Waterloo (arr 0255 and 0439)
0006 and hourly to 0506 Victoria - Gatwick Airport and vice versa (calling at East Croydon both ways, up but not down trains listed as calling at Clapham Junction)
These were arguably the only true 'all night' services but there were other on-off trains (I'm counting anything that was out between 0100 and 0400) including -
2237 Weymouth - Waterloo (arrive 0336)
2252 Waterloo - Weymouth (arrive 0332)
0102 Holborn Viaduct - London Bridge - Orpington (via Bromley North and back to Grove Park)
0135 Eastleigh - Portsmouth + Southsea
0140 Waterloo - Salisbury - Yeovil Junction
0245 Waterloo - Eastleigh - Bournemouth / Portsmouth Harbour (appears to divide at Eastleigh)
0300 Victoria - Rochester - Margate - Ramsgate
0320 Victoria - Brighton
0327 Victoria - Eastbourne
0330 Victoria - Sevenoaks - Tonbridge - Ashford - Folkestone
It's possible I may have missed something, and the above are Mon - Fri times (some were different on Monday mornings)
Some of the longer distance trains are marked as 'second class only' implying a few loco hauled coaches along with parcels or newspaper vans.
No mention of anything on the Holborn Viaduct - Wimbledon / Sutton lines in this timetable.
I believe there may have been more night trains towards Orpington at one time - a friend who's a bit older than me says that his family moved from Orpington to Benfleet at one stage, his father had been in a 'Fleet Street' editorial role, and the night train service to Orpington was reduced. This in turn implies that there was some sort of night service on the Fenchurch Street lines at some point.
I can remember London Buses issuing some 'buses for night owls' booklets in the early to mid 80s, once they realised the night bus network might be worth letting people (other than the people who already knew about it) know it existed, and some included overnight (or very late / early) train services - I remember the Kingston 'roundabout' services appearing in at least some editions, but can't say for sure when it ended.
In terms of places north of the Thames, I have an idea there may have been some night trains round Manchester, and on the Newcastle / Tyneside lines that got turned in to the Metro, but I don't have anything to hand that gives detail.
The operating day on many suburban lines was quite long, last down train leaving terminus close to 0100, and first arrival around 0500. It's also possible there were staff / 'not advertised' trains later and earlier - I only have a public timetable to hand.
There was also the 'Inter Station Bus Service' (more on London Bus Route Histories website
here) which I understand was originally operated under contract to the railway companies (it started in the 1930s - a private company ran it before London Transport took it on in 1936) so is only a slight tangent to this thread - it ran in that form until 1985, and from what I'm aware, it did not use the standard LT buses fares structure (I don't know if any forms of rail ticket were valid on it.) One of the core markets for it (hence latterly operating Sunday night only) was service personnel travelling back to base after weekend leave.