What exactly does "nights" means when you book? Is it number of night you are going to sleep, or simply days you are going to stay?
Accommodation bookings count the nights you spend simply because that's what you need accommodation for: to sleep. This is based on the somewhat valid assumption that your main night time activity is sleeping.
I understand where the confusion might arise from between day and night counts. Because nights are interposed between days you think you are staying for 1 day more. However consider that usually check-in time is in the afternoon and check-out is in the morning so effectively you are occupying the accommodation for the exact numbers of hours (computed as
nights * 24h) you booked it for. To this purpose consider a realistic 3 night booking with check-in at 3pm and checkout at 11am. Total booking time is
2 * 24 + 20 = 68hwhich is
~ 3 days.
Your 7-Night Reservation
You say you plan on arriving on the 1st December and leaving on the 8th of December. That equates to a booking of 7 nights. Since you mention an arrival time of 10am, the actual check-in time depends on the hotel/hostel. Most of these usually check guests in in the afternoon, to leave time between check-outs to clean the rooms. Check-out times tend to be before noon, for the same exact reason. To be sure, ask the hotel for specific check-in and check-out times.
However, if you arrive before your room is ready you can most definitely ask for them to keep your luggage whilst you go to the nearest pub for a good old English breakfast. This should be a free service.
As mentioned in the comments below, if you desperately need the room for 10am because you want to shower/sleep then you might have to book for an extra night (the one between the 30th November and 1st December). If you do so make sure you tell the hotel you will be arriving on the 1st rather than on the 30th, to ensure they don't consider it a no-show and cancel your booking (most probably after charging you for the whole amount nonetheless).
Note that, if the OP wants a *guaranteed* check-in time of 10 AM, they must book the previous night as well (8 nights) -- otherwise they run the risk of having to wait until 3 PM to be able to check in.
@jpatokal That depends entirely on what hotel chain, and where. Many hotels offer free late-checkout and early-check-in, if you request it. Sometimes they can only grant the request if shortly before the booking is due to happen, as they need to ensure noone else is coming in. Still guaranteed is guaranteed, even if you only know for sure a few days before.