I think you must be getting DSA not ESA. Take a look here for the difference
https://www.ucas.com/connect/blogs/grants-and-funding-disabled-students. ESA is for part time students.
Yes you are eligible for housing benefit. But you first need to find out how much you will get. It is not a blank cheque to cover whatever you want to spend. Your student and living loans are considered income so it may be a lot less than you think. Shelter has a good way of calculating this
http://england.shelter.org.uk/housing_advice/housing_benefit/claiming_housing_benefit
Once you know how much you can get, ask your university to help you find something. They may put you in a hall of residence.