Moving house does not automatically end your Housing Benefit, but you must tell your council about the move and provide details of your new rent and circumstances. If you move to another council area, you will usually need to claim from the new council, and your award may change because Local Housing Allowance rates and other rules can differ. If you are of working age, you may need to claim Universal Credit instead, unless an exception applies, such as living in specified supported accommodation. Check the official GOV.UK guidance and contact the relevant council promptly.