I assume the Question is referring to the former one-stop-shop initiative, launched in 1998. I have no information with regard to the operational costs of these offices as this is a matter for each local authority concerned.
Current policy is set out in the Government’s Action Programme for Effective Local Government ; this addresses a range of local government reform measures, and in relation to service delivery, provides for an increased emphasis on identifying customers’ expectations, requirements and experiences. The proposals are designed to promote both increased operational efficiency and value for money through more integrated administrative and implementation arrangements and also to enhance the capacity of local authorities to achieve their broader role of promoting the sustainable development of their areas, the welfare of local communities and the quality of life of individual citizens by virtue of the effectiveness with which they perform their entire range of regulatory, representational and service delivery functions.
Internal organisational arrangements, including utilisation of any existing one-stop-shops , are a matter for individual local authorities to decide.