Quite often when I try to book a single Saturday night at a premier inn
-even weeks ahead, they have no rooms but add a second night )Friday or Sunday) and miraculously they usually then have space.
I book the two nights, securing it on(but not paying with!) a credit card. Making use of their penalty free booking amendment before 1pm on the day of arrival, I phone the hotel and cancel the unwanted night.
Always seems to work.
Note that you do have to phone in person and speak to reception, their website is designed to reject online requests to do this.