You'll just have to choose between whether you want to be potentially identifiable or whether you want to make it known that there is a certain percentage of people with your specific circumstances/situation (who might need particular services, or be likely to vote for particular policies).

If you're unique enough to be obvious from a postcode and census answers then I don't really see how you can definitively avoid identification without removing potentially useful data (i.e. you'd have to remove/generalise questions or move to a higher level location category). It's a bit of a balancing act as evidenced in this thread with you worried about specificity while ada wants to narrow things down even more.