References from previous landlords will go in your favour. Many people will apply for a property and what you do is not as important as having a steady income. Disability payments are as regular as clock work. I have rented many places but I normally stay there for a long time and that's what land owners like. Estate agents will also have a range of vacant properties which they want to getting some return on. Tell them how long you lived in the cabin and the owner died. Maybe you can get somebody else that the agent can ring to back up what happened.

You will find a place to live. It will be the right one.