The 1970 Western Region timetable shows 6 sleeper trains leaving London Paddington in 24 hours on Fridays/Saturdays 12/13 June to 4/5 September.
These are
22:55 to Penzance Friday Only (Sleeping Cars for Isles of Scilly passengers ONLY)
23:45 to Penzance (Sleeping Cars and Motorail detatched at Exeter St Davids)
00:50 to Milford Haven (Sleeping Car passengers ONLY)
00:55 to Penzance (Sleeping Car passengers only, Motorail to Plymouth & Penzance
01:25 to Swansea (Sleeper Car Passengers for Cardiff could travel via Swansea upon payment of a Swansea to Cardiff single Ticket.
21:30 to Milford Haven Saturday Only.
Bit cheeky to state the 21:30 as it's the Daily sleeper to South Wales that ran earlier on Saturdays

And there was also the 19:25 SX Bristol TM to Newcastle Sleeper.