When I used to work at Euston and Kings Cross, I would regularly see sleeper staff coming into and out of the various hotels in the area.
I have also seen Eurostar staff use the Premier Inn in York Way, Kings Cross.
One quick diversion on how it was done in the past in Italy
(not sure how many sleeper trains still run or if this was still the arrangement right up until Covid)
About ten years ago I was doing an on-line search to find a moderately-priced hotel in Rome.
One option offered at a lower-priced, but not rock-bottom, hotel near Termini involved you having no access to your room during the daytime between 8am and 8pm.
Apparently the deal was that your room (and your bed / shower) was used during the day by a sleeping car conductor who had arrived in Rome in the morning on an overnight train.
By 8pm he would have headed back to the station for his next shift, and you got your room back for the night!
The hotel was quite open about this arrangement and mentioned the "sleeping car conductor" bit presumably as they thought that made it sound a bit more reputable or legitimate. They didn't mention whether or not the room got cleaned and bedding changed twice a day as part of the deal.
Needless to say, my wife and I did not take advantage of this economising hack.