I've got a WA9 postcode. Last time I checked, I didn't live in Warrington. If you pay your council tax to St Helens, you're in St Helens. If you pay it to Wigan, you're in Wigan. If you pay under Warrington, you're in Warrington.
Postcodes are meaningless. Rainhill has an L35 postcode. It isn't in Liverpool