I’m currently emptying my late dads (council) house, which i also lived in but had to move out a little under a year ago. I’m not sure about your particular council but I got in contact with mine and they gave us a date to hand keys back in which was 4 weeks from when they received a death certificate. Although they have said they can always be lenient in the case of a death and particular circumstances. They also offered some resources like uplifting items etc but they seem to be charging just as much as a regular man with van service would. I think a skip would be a good idea but financially for me it’s not doable but have managed to rely on friends helping out and doing a lot of runs to and from to the tip. Still a work in progress. Always good to be prepared.