Don't register with an NHS doctor -- they have heaps of sensitive and very specific info about individuals, increasingly stored very centrally.
Don't get a credit card, or get a bank account, or use Paypal, or apply for a supermarket loyalty card, or do anything that might fetch you up on Experian's database.
Don't send your kids to a state school. The LEAs have heaps of info, including all about household income, children's medical needs, their parents' residence and marriage status, etc.
Don't apply for tax credits -- actually, don't get into the PAYE system or do self-assessment. Way too sensitive data you're giving away there.
I could go on and on...