I am in the same position as you , so I can relate . I have been told by the Gingerbread helpline and I have checked myself , as I am working part time I could get help from universal credit to pay my rent, as my salary it is not enough to cover all the housing costs. I guess , the tricky part would be to find a landlord who is happy to let their property to someone claiming benefits but hopefully I’m wrong !
Please , ring the gingerbread helpline , they are indeed very helpful . All the best !