Postcodes and local authority districts

[alanski66]

I was looking for a relationship between postcodes and local authority district names what ONS seem to call LADNM here:
https://www.data.gov.uk/dataset/afc2ed54-f1c5-44f3-b8bb-6454eb0153d0/lower-layer-super-output-area-2001-to-lower-layer-super-output-area-2011-to-local-authority-district-2011-lookup-in-england-and-wales

There seems no obvious returned data that matches what some call the admin district. An example might be "NN18 0ES". This returns https://api.postcodes.io/postcodes/NN180ES

I thought the admin district might be the closest link the local authority district but for this postcode admin district returns North Northamptonshire'. Am missing some important glue or into a gray zone of ONS history and unknowns?

[francisbarton]

Is North Northamptonshire not the correct name for the LAD?