Promoting a comment to an answer
I think what you want is a Day Use Rate. Not all hotels offer them, but many do, especially around airports.
As the name suggests, it's the use of a room in the hotel during the day, but not overnight. Typically, you'll have to be out by late afternoon, so that the room can be cleaned in time for a guest to use it from that evening. Unlike a normal reservation, they allow very early checkin.
If you do a hotel search on many (but not all) portals, for checking in and out on the same day, then day use rates will come up, such as shown here for next week near Heathrow:
If you can't find something suitable, it's often worth ringing some hotels near where you want to be, and ask if they offer Day Use rates. As long as they have housekeeping staff around for long enough, and enough people who check out early, they'll most likely do so. (Resort type hotels where most people stay as long as possible won't)
Cost wise, it's normally cheaper than a night at the hotel, but not always. It'll always be cheaper than two nights at the hotel, which is otherwise you only other easy way to get a checkin around 6am and not have to check out before about 11am!