Are all local bodies constituted by a State or Central Law regarded as local authorities for the purposes of the GST Acts

No. The definition of ‘local authority’ is very specific and means only those bodies which are mentioned as ‘local authorities’ in clause (69) of section 2 of the CGST Act, 2017. It would not include other bodies which are merely described as a ‘local body’ by virtue of a local law. For example, State Governments have setup local developmental authorities to undertake developmental works like infrastructure, housing, residential & commercial
development, construction of houses, etc. The Governments setup these authorities under the Town and Planning Act. Examples of such developmental authorities are Delhi Development Authority, Ahmedabad Development Authority, Bangalore Development Authority, Chennai Metropolitan Development Authority, Bihar Industrial Area
Development Authority, etc. Such developmental authorities formed under the Town and Planning Act are not qualified as local authorities for the purposes of the GST Acts.

(FAQ 5: GOVERNMENT SERVICES)