If you don't have the required documents for housing benefit or council tax reduction, there are alternatives you can consider. Based on available council records, if you lack a National Insurance number, you can apply for one through the government website. Additionally, for certain situations, such as voting without photo ID, you can apply for a Voter Authority Certificate issued by the council free of charge.
For housing benefit, check this link for guidance on document submission: Submit documents for housing benefit.
If you're unsure about specific requirements, it's always a good idea to contact your local council for assistance.