This is likely to be your largest outgoing. Most first year students at Durham University live in college accommodation, and details on college accommodation fees can be found here:
Residence Charges - Durham University
This can be a good choice to help you plan your finances as you will be close to your lectures, therefore should not incur additional travel costs, and fees are usually inclusive of water rates, gas/electricity and broadband internet. Some colleges are fully catered, meaning that meals are also included with your college fees.
Another option would be to rent privately, perhaps sharing with other students. Rents can vary widely depending on the location of the accommodation. Again, some landlords will include water and energy bills with your rent, which can help you to plan your finances. It is advisable to arrange accommodation prior to arrival, and this will also help you to plan your budget as you will be aware of how much you need to pay.
Aim to pay your college accommodation fees as soon as possible or set aside sufficient funds. This is likely to be your largest outgoing so ensuring that this is covered will help you to see how much money you have remaining for the rest of term. You can then divide the remainder of your income over the number of weeks in the term, to give an idea of how much you can spend each week.