Private renting is often the easiest way to being rehoused as you can choose the property type and location.
Check with local estate / letting agencies and search online, popular websites include, Rightmove & Zoopla.
If you're worried about being able to afford the rent in a private tenancy due to being on a low income check the local housing allowance which is the amount of financial help you could get https://lha-direct.voa.gov.uk/
For advice and tips in private renting, read the How-to-rent checklist