No hotels - you are thinking of Eurostar!
No taxis I don't think - there certainly never used to be.
When the earliest shift got moved from 05:45 to 05:12 they would let you claim mileage on your car for that shift only but no taxi. (You get free parking underneath St Pancras). Since then the earliest start moved to 04:29 but I see from post above it's 04:54 now - not sure if they got a taxi out of that? Maybe Abellio are better than Stagecoach, but I dare say it's the same stingy people at Derby head office making the, "Why should they?" decisions.
Nights were moving trains around at Cricklewood to be refuelled (there is a person there who hooks up the pipes, records how much each pump dispenses, and liases with tanker lorry drivers, so you don't do any of that). Should get about three hours dead time after fuelling has been done, so take a sleeping bag/blow up bed.
The Saturday night shift mentioned above is new - I'll speculate and say it might not involve refuelling, and might go to Corby/Kettering, but I'm just guessing. There was a nightshift to Leicester, ECS to Derby, and back years ago.
Sundays in the working week - Last roster I saw was about 10-12 Sundays a year, so pretty good.
There were more AM shifts than PM shifts, but these were arranged so that the later starts (8,9,10am type starts) were on alternate weeks to the early AMs.
Typical work:
I dont know the current diagrams, but it used to be the following sort of thing:
Corby and back, Nottingham and back, or the other way around.
Sheffield and back.
Nottingham and back, Cricklewood sidings and back in a taxi.
Nottingham, pass to Derby, then to Sheffield and back to London.
Nottingham or Derby (both about the same distance) and back twice. You could only be rostered two of these in a week (unless you did rest day work).
I believe Rest Day Work is time and a half now.