Housing analysis results by Durham University:

According to the Summary of the Durham University in-year analysis of student housing supply and demand it is expected that there will be enough accomodation for everyone in durham with rooms to spare. 

Extract from the summary page:
In 23/24 the University had a total of 21,588 students, of which 20,814 were full-time. Looking at our position on the capacity of the city at the start of 23/24, and comparing this to the in-year analysis we are confident that our numbers stand up to scrutiny.
There has been enough accommodation in the city for everyone who wanted this year. There were 18,448 students living in the City in 23/24, and we estimated around 350 bedspaces would remain available in the city.
In 24/25 planned total student numbers are expected to be similar to 23/24, however actual total student numbers for 24/25 are not released until after the 1 December census date. We do know that there has been enough accommodation in the City for the 24/25 academic year for everyone who wanted it, and sought to secure accommodation for the new academic year. In fact, there were still at least 100-200 vacant bedspaces being advertised in September.
Total student numbers for 25/26 are expected to be similar to 24/25, and so it can be reasonably expected that demand for accommodation in the City will be similar to this year.
Taking all this into account and considering it against forecasted student number data for 25/26 we are confident there will be enough student housing in Durham City to meet demand.
 

Last years' bedspace capacity in Durham 

There were still about 300 houses advertised on StuRents on the 2nd of May 2024 (Figure1). A bit later in the year some properties were discounted up to 10 pounds per person per week. Palatinate first reported on it and also covered it in another story later. There were 247 properties (figure 2) available for 24/25 still in early September 2024.

Here is a screenshot from Sturents at the time: