Yes you will. Being a member of the Local Government Pension Scheme does not affect in any way your entitlement to the basic state pension. However, whilst you remain a member of the Local Government Pension Scheme, as with all pension schemes that are 'contracted out', you will not be contributing to the additional element of the State Pension known as the State Second Pension (S2P). This element used to be known as SERPS.
More details regarding your state pension can be found at The Pension Service website, please see our Other Useful Sites page.