I'm not sure whether I'm on the right track (no pun intended!), but how about Llandovery (assuming it meets the criteria)?
Travelling on Monday, the first service with a connection to London is the 12.38 to Shrewsbury (13.13 - 15.32). It's then necessary to change at Wolverhampton (16.07 - 16.14) and Stafford (16.27 - 16.41), arriving at Euston at 18.03.
There's no return train that night, so you'd have to wait until Tuesday, when you have a choice. Your first is from Paddington at 07.48 to Swansea (10.34 - 11.14), arriving at Llandovery at 12.36 - two minutes short of 24 hours! The second is from Euston at 09.10 to Crewe (10.45 - 11.11) then to Shrewsbury (11.42 - 12.04), arriving at Llandovery at 14.16 - 25 hours and 38 minutes!
The journey from London and back is comparatively short, as it can be done on one day. It takes 5 hours 26 minutes out via Crewe and Shrewsbury, and there's a choice for the return - via Swansea (4 hours 37 minutes) [Total 10 hours 3 minutes] or via Shrewsbury, Birmingham New Street & Moor Street, which takes 6 hours 12 minutes [Total 11 hours 39 minutes].
Someone's going to tell me that it doesn't count now … but that's life!