I've been searching all over, but cannot find a database/CSV for matching a UK Town to postal sectors.
Hampton Hill” is postcode sector” TW12 1
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Ordnance Survey Open Names (open data) gives you postcode and populated place, where populated place is a city, town, village, or some other place where people live.
SW1A 1AA -> City of Westminster RG4 7LR -> Caversham OX1 1AA -> Oxford