Privacy concerns is not ONLY about having your data stored ...
Your private data has to be stored by many different companies and agencies, and I have no problem with that in principle.
The big concern however is having a whole heap of data dealing with many different and unrelated aspects of your life that is easily accessible (and searchable) by a single person or machine. This is when algorithms can be used to look for patterns - often adding 2+2 and coming up with 5.
My travel history, online purchasing history, previous addresses, credit card score, medical history, utility usage, what licenses I hold, any criminal records, my social media contacts, all my family members, what films I have downloaded, what newspapers I read, what YouTube videos I have watched, what languages I speak, which radio and TV programs I prefer, what groceries I buy, which places I visit to socialise and be entertained, my income and outgoings etc. etc. ... these may well all be stored in the databases of various companies and organisations - but it should not be possible for anyone to easily access all those things at the same time because this is when computer algorithms can and inevitably will be used for both specific and speculative searches that result in all sorts of incorrect "hits" and "profiles". The government's wet dream of having everyone's personal details stored in a single indexed central database is extremely dangerous - and is the biggest objection I had to the national ID card. i.e. not the card itself, but the database that would be created behind it.