Housing Benefit and Council Tax Benefit are government schemes to help you pay your rent & Council Tax they are worked out and paid by local authorities. Other welfare benefits are paid through other agencies.
For example the Job Centre Plus deals with Income Support; H.M. Revenues and Customs with Child Tax Credit and the Pension Service with Retirement Pension and Pension Credit.
In Stockport, the service that deals with Housing Benefit and Council Tax Benefit also deals with Free School Meals and School Clothing Grants and Leisure Key.