So many different qualifiers for this thread! However let's choose just a few!
Maximum miles in a 24 hour period:
1,083 miles and 20 chains. Starting from Cardiff Central to Abergavenny, then HST to London via Evesham, over to Cardiff and back to Paddington, over to Swansea and back, then finishing with Paddington to Swansea via Bath Spa, Dr Days Curve, reversal at Bristol Parkway then to Cardiff, then Ninian Park before returning to the mainline to Swansea.
That started at 0400, finished at approximately 0217 the following day.
On an ALR in 2011, though, I managed even more than that, around 1,103 miles, but that was over a 27 hour or so period. No doubt there's higher figures than that in my 2011 or 2012 ALR records but none of them fit truely the 24 hour period.
Longest single journey in a day:
March 2007 (or at least so the general consensus is at this time, one day I'll find out for sure so I can fix the incredibly BIG gap in my RailMiles!):
Hereford > Newport > London Paddington > Circle line Paddington to Kings Cross St Pancras > London Kings Cross > Inverness
With delays caused by signalling problems at Darlington, which had a knock-on effect on the Highland Mainline, we were at least 36 minutes late arriving into Inverness. I have it stuck in my head we arrived at 2044 and were due at 2008. I can't honestly remember for sure what time I left Hereford somewhere between 0745 and 0845 is all I can remember at the moment (for some reasons the notes from my trip, one of the biggest of all time, are missing and have been for years) so let's call it 0844 leaving Hereford and a 12 hour trip. As I don't have it logged on RailMiles, I don't have exact figures but I'd estimate that to be a fair bit over 700 miles.
I would have used my travel back from Scotland to Hereford from last week (weighing in around 570 miles, not including all the leaps around London between arriving and leaving), but strictly speaking the journey didn't start in Edinburgh, it started in Dunblane, so doesn't count.
I'm also struggling to think of anything else where I was heading in one direction, with no doubling back or returning the same day. Definitely by rail only, that one's taking some beating.
Highest mileage day return trip:
After much finding, and no doubt there's better in my records but my recording of moves was poor for a long time, the best I can find currently is 406 miles and 23 chains on 18th October 2005. Swansea > Newport > London Paddington (I have no idea why I changed HSTs!), coming back on one HST Paddington to Swansea. The same day I have it logged as having 313117 from Clapham Junction to Willesden Junction (no logged journey of how I got to Clapham Junction!) then the Bakerloo line to Harrow and Wealdstone for 321419 back to Euston with Silverlink.
That'll have to do I'm afraid, I could be here for a long time otherwise!