You probably need to look at the bigger picture - not just focus on the postcode.
Firstly if it makes it identifiable it's all personal data -not just the postcode.
But, secondly, if what you say is accurate it sounds like data is being aggregated to target individuals for intervention. If that is the case it is hard to see how it can be regarded as anything other than personal data. There may well of course still be a valid legal basis
Conversely if that is not the intention, and the aim is just to identify areas for intervention e.g.via GP surgeries or ward based funding initiatives it is hard to see how the full code can be necessary.
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