The processing time for Housing Benefit eligibility claims can vary depending on your local council and the complexity of your application. Generally, claims can take anywhere from a few weeks to several months to process. It’s important to ensure that you provide all necessary documentation and information to avoid delays. If you haven't heard back within the expected timeframe, you can contact your local council for an update on your claim status. For more detailed guidance, visiting the official gov.uk page on Housing Benefit may be helpful.